The general logic is as following:

Damage reduction is set to Toughness stat.

Defense is added/subtracted from reduction via (incomingDamage * log(defense / 10 + 1) / 5).
(prior to recent update the last number was 3.2 instead of 5)
Now, assuming that you don't want to pull up a calculator for this, what this means is:

• 0 defense has no effect on damage reduction
  
• 5 defense cuts 8.11% of damage
  
• 10 defense cuts 13.86% of damage
  
• 15 defense cuts 18.33% of damage
  
• 20 defense cuts 21.97% of damage
  
• 25 defense cuts 25.06% of damage
  
• 30 defense cuts 27.73% of damage
  
• 40 defense cuts 32.39% of damage
  
• 60 defense cuts 38.92% of damage
  
• 85 defense cuts 45.03% of damage
  
• 100 defense cuts 47.95% of damage
  
• 200 defense cuts 60.89% of damage
  
• 300 defense cuts 68.67% of damage
  
• Negative defense subtracts from damage reduction (but keep in mind that this is still after Toughness was added)

As can be seen, defense grows gradually less efficient, which both means that it doesn't make sense to get your DEF too high, and also that having deeply negative defense won't even get you hit for 2x damage.

Damage reduction is subtracted from damage.
If damage is less than 1 after this, it's set to 1.

• Burn causes 4 damage every second for 3-4 seconds.
  
• Poison causes 1 damage every second for 10 seconds.
  
• Electric causes target's armor to be ignored for 4 seconds.
  
• Stun prevents target from moving or attacking for 1 second.
  
• Frost slows the target for 5 seconds.

Elemental stats displayed on items and acquired via food add up as a % chance to apply the according debuff.

Elemental resistance cuts into probability check, which is
"if random number between (target's resistance) and 100 is less than (chance to apply debuff), apply debuff"
So, if target has a 15% chance to apply poison, and you have 10% poison resist, the odds of getting the debuff would be (15-10)/(100-10) = 5/90.
Unfortunately, numeric values for resist stats aren't shown anywhere, so it is not clear whether this is worth pursuing as such.

Both Evade and Block stats offer a fixed chance to avoid damage completely.

This comes off as an interesting combination aside of normal defense/toughness stats, as it is possible to get your evasion up to 70..80% by the end of the game via food alone.

A thing to note, however - for damage sources that can hit multiple times (mostly beams of various kinds), if you evade the first hit, you can still be hit subsequently.

The above have been derived by inspecting the game logic using ILSpy. Related calculations were found in Creature.Hit.