The most important things first: I am not a natural speaker of the English language, so there might be grammar errors in this guide. Pointing out the most egregious ones will be appreciated.

Hello and welcome to my very first guide on Steam, Citizens of the Internet!
Intended for new and regular but not-really-advanced players, this guide will show the roles each Hero can fulfill, his/her strengths and his/her weaknesses. Noteworthy cards, basic strategies and possible combos will also be discussed.
By no means is this a complete guide. If you have some cool stuff to share for this guide, don't hesitate to do so. Of course, you'll get credited for your discoveries.

All pictures are taken from the official site of the original tabletop version of SotM: http://sentinelsofthemultiverse.com/

Work in Progress

Complexity: 3
Roles: Nuker, Off-Tank, Field Control
Strengths: One of the strongest Heroes if prepared, can delay many Villain Cards with "Sub-Zero Atmosphere".
Weaknesses: VERY vulnerable to Equipment- and Ongoing-Wipes, more so than most other Heroes. Several One-Shots hurt him if he's not prepared.

The only Hero of the base game that has a complexity of 3 and for good reasons! His innate power is completely useless without his Module-cards and deciding when to prepare and when to strike will be crucial for everone trying to master him. That said, AZ profits from several unique interactions with himself thanks to his two Modules, using Fire damage on himself to deal Cold damage to someone else (including himself) and using Cold damage on himself to get healed.
The modules are also the reason why Damage Enhancers are really great on him, since the efficiency of them are multiplied for AZ. For example, Legacy has used his innate power Galvanize, which increases damage from Heroes by 1. This means that AZ, if he inflicts Fire Damage on himself, will receive 1+1 Fire damage. This turns into 2 Cold damage that is, again, increased by 1. In addition, AZ has several One-Shots that deal damage multiple times, the most famous one being "Hoarfire", so you really want Damage Enhancers with AZ, even if he's supposed to be a Tank.

When incapacitated, his three abilities are rather standard: Activate Power, increase next Damage dealt by chosen hero by 2 or destroy a target with 1 HP.

Complexity: 2
Roles: AoE, Nuker, Off-Tank
Strengths: His Modes make him very versatile. Can immediately start to deal decent damage despite being a preparation-based Hero. The only Hero capable of using 3 Powers in a single turn by himself. Almost immune to Ongoing-Wipes, especially if he has copies of "Ammo Drop" in his hand.
Weaknesses: Only one main damage type (Projectile). Very susceptible to Equipment-Wipes. Can only receive suboptimal support when using one of his Modes. Also negative effects when drawing cards.

Bunker, who's not a robot, is one of the faster characters despite his appearance and can adapt to most situations, usually by shooting stuff and letting things explode. Even though he relies heavily on Equipment, it's his four Ongoing-Cards that utilize them to their full effect, "Ammo Drop" and his three Modes. To use Bunker effectively, one must learn to make the most out of those cards while also know how to amass a large hand of cards.
"Recharge Mode" is mainly used in situations where the threat is manageable to stock up on cards, but also has great synergy with both "Gatling Gun" and "Omni-Cannon", since they rely on passive discards to work. The "Recharge Mode" + "Gatling Gun" + "Omni-Cannon" combo is almost guaranteed to show up when playing Bunker as a damage sponge.
"Upgrade Mode" shortens the amount of time Bunker needs to prepare for massive damage, but can also be used to play an One-Shot every turn while preparing Bunker at his usual pace. As a side-note, one should think about using two "External Combustions" in a single turn if there are several high HP-targets to worry about.
"Turret Mode" is where Bunker becomes recklessly aggressive. His hand turns into pure ammunition for "Gatling Gun" and "Omni-Cannon" and only "Ammo Drop" allows to draw cards anymore, but using two Powers each turn (three if "Auxiliary Power Source" has been prepared) with enhanced damage more than makes up for it. Especially since Turret Bunker is very likely to destroy at least one or two Villain Cards each turn.

His incapacitated abilities are also great: Playing a card, reducing the next damage received by target hero by 2 or taking a card from the trash into the hand.

Complexity: 2
Roles: Steady Damage, Field Control
Strengths: Has many options to damage and/or shut down targets by redirecting or negating damage done by them. Very strong against Villains with few HP-less cards. Has many damage types and her main damage type Radiant is rarely resisted against.
Weaknesses: Many cards require her to sacrifice cards or HP. Also Megalopolis, since it's cards usually block her more exotic upkeeps (like required damage dealt in the case of "Zealous Offense").

Fanatic is reckless. Really reckless. But she usually can afford this kind of recklessness thanks to her high HP, cards that recover a small amount of HP, "Undaunted" and "Aegis of Resurrection". And most of the time, shutting down the high-damage targets is usually worth the sacrifices. Still, Fanatic can only be reckless for a limited amount of time. If there's no imminent danger, then it's usually better to deal damage that doesn't require her to sacrifice too much.
To be honest, it's hard to give general advice for Fanatic since many of her cards are highly situational. At the same time, this is also her greatest strength, since it allows for a good amount of flexibility. Unlike AZ and Bunker, she can react to many threats immediately. Even with "End of Days", which is great if the Villain becomes nigh-unmanageable otherwise or if another card just wiped the field anyway.

Her incapacitated abilities reflect her dual nature: Playing a card, healing 2 HP or increasing the next damage dealt by chosen hero.

Complexity: 1
Roles: Steady Damage, Environment Control, Tank
Strengths: Deals a good amount of damage every turn. Has many cards that allows him to draw cards. Can prevent cards from going into the trash with "Savage Mana", therefore weakening most Villains.
Weaknesses: Almost always uses Melee damage. Relatively inflexible once his strategy is in play unless a Haka is used. Innate Power is more of a safety-net than something that synergises with his deck. Needs to discard a lot of cards during the game.

Haka is very simple even for Complexity 1-Heroes. Usually, there's no card that isn't worth playing right now for him. It also helps that he gets a lot of cards during play AND has a relatively low card variety (14 different cards in his deck), therefore it's recommended to use a Haka-card sometimes to beef him up, but leave at least one Haka in the hand just in case the Villain or Environment has something nasty up his/her/it sleeve.
But even with that said, there are some cards that will make or break a game as Haka. "Ground Pound", "Rampage" and "Savage Mana" all rely on timing and "Punish the Weak" can be both a blessing and a curse. If one plans to focus on "Punish the Weak", then a Nuker is required for the team for the strong, high-HP targets that shows up sometimes with several Villains. Haka is good against small targets, not against something like "Citizen Anvil", "Citizen Truth", "Electro-Pulse Explosive" and most Environment cards with HP.

His incapacitated abilities allow for a lot of control: A player may draw or play a card or reduces the next damage received by 2.

Complexity: 1
Roles: Tank, Support, Situational Damage
Strengths: Protects and empowers his team easily. Impressive defense against both low- and high-number damage. Has one of the best heals in the entire base game thanks to "Motivational Charge". Very resistent against Equipment-wipes.
Weaknesses: Can only deal Melee damage. Vulnerable to Ongoing-wipes. Most damage cards are One-Shots. His best cards require him to deal himself damage. Innate Power also increases self-damage from Heroes.

Legacy isn't called "America's Finest Legacy" for nothing. He's the archetypical leader who will take anything for the team, increases the overall damage of the entire team with ease and can even prevent some of the nastier effects thanks to "Danger Sense", "Heroic Interception", "Lead From The Front", "Next Evolution", "Take Down" and the fact that "Surge of Strength" is a low-priority Ongoing, making it a good target for single Ongoing-discards.
Using Legacy as a mere meatshield would undermine his greatest strength, though. With the exception of the low-damage "Motivational Charge", he can only deal damage with One-Shots, but these tend to be really strong.
With all that said, Legacy tends to get incapacitated first, but one would be wise to make sure that that won't happen early. His supportive qualities are too great to be ignored and even though Legacy has good incapacitated abilities, he's better off leading the team towards victory with his own fists.

Speaking of incapacitated Legacy... He can either allow a player to use a power or draw a card or he can reduce the damage dealt by Environment cards by 2 for a whole round.

Complexity: 1
Roles: Nuker
Strengths: Deals huge amounts of Fire damage. "Summon Staff" is useful even if Ra's staff is already in play. Can handle a large group of targets with ease.
Weaknesses: His only main damage type is Fire and dealing Projectile Damage requires to sacrifice the card that increases his power. Doesn't do much aside from dishing out Fire Damage.

Ra's main draw is the high amount of damage he can dish out. While others, like AZ, Bunker and Tachyon, might have a much higher potential for damage, they also need a lot of preparation and won't explode until mid-to-lategame. Ra is perfect for early-to-midgame since he doesn't need a lot of preperation to clean up the Villain field.
At the same time, Ra also has a surprisingly high number of ways to incinerates the foes foolish enough to stand against a human demiurg. "Drawn To The Flame" is great against Villains who both unleash a lot of minions and have some Ongoing cards up their sleeve, "Scorched Earth" is the same but measuring it's strength in the number of Environment cards instead of Ongoing cards and "Wrathful Gaze" is useful when the puppet master-esque Villain has annoying minions with low life that have a lot of damage reduction or even immunity going on.
Ra can also push his divine powers to the limits with "Imbued Fire", which increases Fire Damage by 1 and changes all hero damage to Fire, and "Solar Flare", increasing his own Fire Damage by 2 at the cost of having to receive 4 Psychic damage each turn. Combined with "The Staff Of Ra", something that usually is easily avaible, his "Inferno" would be truly devastating, dealing 3+4 damage to a target and 1+4 damage to up to 5 other targets. This is the power of the sun too hot to handle even for Citizen Dawn.

If the everlasting sun should ever turn into a white dwarf, he can allow a Hero to use a power, put an Environment card in play on the bottom of the deck or destroy an Ongoing card.

Complexity: 2
Roles: Steady Damage, Field Control
Strengths: Becomes stronger the longer the game goes on thanks to her "Burst"-mechanic. Can play several One-Shots in one turn. Relatively resistent against Field Wipes.
Weaknesses: Low HP and no way to heal herself. Her only Equipment-card is very valuable. Her lategame-nuke deals Melee damage. Overly long games will turn her Trash into her new deck, instantly resetting her Burst mid-game.

Tachyon is all about throwing out cards and utilizing her superior speed to great effect. She can draw a lot of cards with "Fleet Of Foot", "Nimble Strike", "Pushing The Limit", "Quick Insight" and "Research Grant" . Several of those freshly-drawn cards can also be played within a single turn thanks to "Fleet Of Foot", her trusty "HUD Goggles", "Lightning Reflexes" and "Pushing The Limits".
A good number of her cards deal damage across the board, "Hypersonic Assault" even prevents the inflicted targets from dealing damage until her next turn. And if some damage gets through to her, she can prevent it with "Synaptic Interruption" or retaliate next turn with "Supersonic Response". Is there a nasty Environment or Ongoing card to deal with? "Blinding Speed" solves that problem.

Why you should play several cards in a single turn? Because most of the cards I've just mentioned (and some more) are "Burst"-cards. Both "Lightspeed Barrage" and "Sonic Vortex" profit from a high number of Burst cards in your Trash, with the former dealing more Melee damage and the latter dealing 3 Sonic damage to more targets.

There's no reason to slow down if she gets incapitated, though. Allowing a player to either draw a card, play a card or take a card from the trash back into the hand is too good to ignore.

Complexity: 1
Roles: AoE damage, Nuker, Support, Field Control
Strengths: Deals a lot of damage every turn, both Lightning and Projectile. Can adapt to many situations. Destroys Ongoing- and Environment-cards with relative ease. Almost immune to Equipment-wipes.
Weaknesses: Very vulnerable to Ongoing-wipes. Rather slow. Can't control some of his damaging cards, which can be disadvantageous at times.

Overview avaible soon

Complexity: 2
Roles: Support, Field Control, Deck Control
Strengths: Can manipulate the entire game to her advantage and weaken Villains and Environments by putting potentially dangerous cards to the bottom. "Twist The Ether" is one of the best Damage Changers. Can help Heroes in a pinch if they have a bad hand. "Telekinetic Cocoon" plus "Demoralization" and/or "Wrest The Mind" is a very strong combo. Immune to Equipment-wipes.
Weaknesses: Very vulnerable to Ongoing-wipes. Can only deal Psychic damage.

Overview avaible soon

Complexity: 1
Roles: Everything. No, really!
Strengths: The most versatile of all base game-Heroes. Can play several cards and activate two powers in one turn.
Weaknesses: Focuses on Projectile damage. Very vulnerable to Equipment-Wipes.

Overview avaible soon