These could also be named 'common' perks, due to them being what you usually get, and having the 'weakest' abilities when compared to green, blue and orange perks.(I will update with photos soon)

Advanced Autoloaders: cannons reload 3% faster.

Asbestos Coating: soldiers are 20% more resistant to flames.

Blast Doors: fire spreads throughout the fortress 15% slower.

Bloodlust: soldier heals +10% for every kill.

Bombardment: all mortar bombs deal 5% more damage.

Camouflage: enemy has +3% chance to miss.

Condensed Napalm: fire from incendiary weapons spreads 10% faster.

Cushioned Helmets: soldiers recover from stun 20% faster.

Death Cloud: neurotoxin kills 20% faster and lasts 10% longer.

Desperate Measures: soldier's death extinguishes fire, dissipates toxins and repairs 10 hp.

Element Of Surprise: 9% longer stun effect duration.

Heroic Sacrifice: soldiers invading enemy base explode in death, dealing 25 damage.

Last Stand: weapons deal +10% damage when under 40% fortress structural integrity.

Lex Storm: HYDRA and BASILISK cannons deal +5% damage.

Lucky Shot: converts 6% missed shots to hits.

Onslaught: all weapons get +9% reload boost whenever a target is destroyed.

Overclocking: Scrambler, Infiltration and Airships prepare +4% faster.

Rapid Ventilation: toxic contamination dissipates 20% faster.

Rocketeering: missile launchers reload 4% faster.

Superconcrete: fortress sustains 4% more structural damage.

Supply Lines: +2 Ammunition production.

Titanium Jackhammers: soldiers tear down enemy equipment 40% faster.

Traitors and Thieves: enemy loses -2 ammunition per second.

Turbocharger: energy weapons recharge +4% faster.

War Hammers: soldiers repair 2% faster.

The green perks, or 'rare perks', have a lower chance of obtaining than white perks but bigger than blue and orange perks. They are 'better' than the white perks, with almost every perk having better stats, but lower than blue perks and 'worse' than orange perks. (I will update with photos soon)

Advanced Autoloaders: cannons reload 4% faster.

Asbestos Coating: soldiers are 30% more resistant to flames.

Blast Doors: fire spreads throughout the fortress 20% slower.

Bloodlust: soldier heals +15% for every kill.

Bombardment: all mortar bombs deal 7% more damage.

Camouflage: enemy has +4% chance to miss.

Condensed Napalm: fire from incendiary weapons spreads 15% faster.

Cushioned Helmets: soldiers recover from stun 25% faster.

Death Cloud: neurotoxin kills 30% faster and lasts 15% longer.

Desperate Measures: soldier's death extinguishes fire, dissipates toxins and repairs 30 hp.

Element Of Surprise: 12% longer stun effect duration.

Heroic Sacrifice: soldiers invading enemy base explode in death, dealing 50 damage.

Hex Aegis: Kinetic Shield regenerates +5% faster.

Last Stand: weapons deal +15% damage when under 40% fortress structural integrity.

Lex Storm: HYDRA and BASILISK cannons deal +6% damage.

Lucky Shot: converts 7% missed shots to hits.

Onslaught: all weapons get +12% reload boost whenever a target is destroyed.

Overclocking: Scrambler, Infiltration and Airships prepare +5% faster.

Painkillers: soldiers gain 6% more health.

Powercells: +1 power supply.

Rapid Ventilation: toxic contamination dissipates 25% faster.

Rocketeering: missile launchers reload 5% faster.

Superconcrete: fortress sustains 6% more structural damage.

Supply Lines: +2 Ammunition production.

Titanium Jackhammers: soldiers tear down enemy equipment 50% faster.

Traitors and Thieves: enemy loses -3 ammunition per second.

Turbocharger: energy weapons recharge +6% faster.

War Hammers: soldiers repair 4% faster.

Blue perks, or 'epic/super-rare' perks, have a lower rate of obtaining compared to white and green perks, but higher than orange perks. However, these are 'better' than white and green due to having in almost every perk better stats. If compared to orange perks,blue perks are 'worse'. (I will update with photos soon)

Advanced Autoloaders: cannons reload 5% faster.

Asbestos Coating: soldiers are 40% more resistant to flames.

Blast Doors: fire spreads throughout the fortress 25% slower.

Bloodlust: soldier heals +20% for every kill.

Bombardment: all mortar bombs deal 9% more damage.

Camouflage: enemy has +5% chance to miss.

Condensed Napalm: fire from incendiary weapons spreads 20% faster.

Cushioned Helmets: soldiers recover from stun 30% faster.

Death Cloud: neurotoxin kills 40% faster and lasts 20% longer.

Desperate Measures: soldier's death extinguishes fire, dissipates toxins and repairs 75 hp.

Element Of Surprise: 15% longer stun effect duration.

Heroic Sacrifice: soldiers invading enemy base explode in death, dealing 75 damage.

Hex Aegis: Kinetic Shield regenerates +6% faster.

Last Stand: weapons deal +20% damage when under 40% fortress structural integrity.

Lex Storm: HYDRA and BASILISK cannons deal +7% damage.

Lucky Shot: converts 8% missed shots to hits.

Onslaught: all weapons get +15% reload boost whenever a target is destroyed.

Overclocking: Scrambler, Infiltration and Airships prepare +6% faster.

Painkillers: soldiers gain 8% more health.

Powercells: +1 power supply.

Rapid Ventilation: toxic contamination dissipates 30% faster.

Rocketeering: missile launchers reload 6% faster.

Superconcrete: fortress sustains 8% more structural damage.

Supply Lines: +2 Ammunition production.

Titanium Jackhammers: soldiers tear down enemy equipment 60% faster.

Traitors and Thieves: enemy loses -4 ammunition per second.

Turbocharger: energy weapons recharge +8% faster.

War Hammers: soldiers repair 6% faster.

Orange perks, also named 'legendary perks', are the perks which are the hardest to get in the entire game. They are supposed to be the best perks out of all the previous tiers, but unfortunately, this is not the case in every perk, having some really underwhelming ones (and also being very overrated in my opinion). Another big difference is that orange perks do not follow the other perks, just normally upgrading the stats from previous tiers, but they are all completely new. Many of them are focused on improving specific rooms. (I will update with photos soon)

Air Superiority: Airships are 15% more durable and move much faster.

Arms Race: NEMESIS Tactical Nuke prepares 10% faster.

Auxiliary Reserves: +1 soldier joins your forces.

Death From Above: TARTARUS Heavy Mortar gains +8% accuracy.

Hard Shell: missiles and shells are 20% more durable.

Jackboots: soldiers run 50% faster.

Maximum Overcharge: big energy weapons SIRIUS and HYPERION deal +30% damage.

Microfiltration: soldiers survive in contaminated zones.

Nuclear Superpower: Nuclear Reactor yields +2 power.

Volunteers: +1 soldier joins your forces.

Wall Of Fire: all active turrets deal +10% more damage.

Locked/unobtainable perks cannot be awarded by any means. They are the most unknown and mysterious perks in the game. They feature the colour red amongst them, thought to be a disadvantage perk. The only way to find them or use them is when the opposing fort or our fort (when playing one that is not our normal but we are forced to use one) has them. All perks except Expendables are not proven to give any sort of benefit/drawback, but most probably be merely cosmetic and have no influence whatsoever in the game. I will update this with the specific levels where each of these perks appear, maybe new information and if possible better quality images.

Expendables: exhausted soldiers work slowly and die fast. (Red perk)

Experimental Prototype: Weapon requires a few tweaks and calibrations. (Red perk)

Praetorians: elite weapon crews shell like there is no tomorrow. (Orange Perk)

Safe Sector: home turf advantage. (Orange Perk)

Warmaster: this fortress is run by a superb military leader. (Orange Perk)

My only theories:
Experimental Prototype: weaker and/or slower utility? It is most probably just cosmetic.
Praetorians: stronger and/or faster and/or healthier soldiers? It is most probably just cosmetic.
Safe Sector: have a similar effect to Camouflage (enemy has +?% chance to miss)? It is most probably just cosmetic.
Warmaster: have an exceedingly better AI? It is most probably just cosmetic.

Icons:
Expendables: same as Praetorians.
Experimental Prototype: same as Turbocharger.
Praetorians: same as Expendables.
Safe Sector: same as the Empire symbol.
Warmaster: same as Strike Commander Belligerent medal.