Immunity doesn't mean you are immune to a certain skill. Immunity is simply a chance that you will not be attacked. The chance is increased by using a stronger weapon.
Acid Immunity
Acid Immunity is a passive skill that causes your pirate to be immune to Acid from Pestilence and Fly Traps
Cursed Immunity
Cursed Immunity is a passive skill that causes your pirate to be immune to Curse.
Note: The Shadow Cutlass is unreleased.
Fire Immunity
Fire Immunity is a passive skill that causes your pirate to be immune to Fire Attacks.
Life Drain Immunity
Life Drain Immunity is a passive skill that causes your pirate to be immune to Life Drain.
Pain Immunity
Pain Immunity is a passive skill that causes your pirate to be immune to Pain and slow effects.
Poison Immunity
Poison Immunity is a passive skill that causes your pirate to be immune to Poison. This includes venom from creatures (Scorpions, Wasps, etc.) and poisons applied to weapons (Daggers, Swords, Bullets, etc.)
Snare Immunity
Snare Immunity is a passive skill that causes a pirate to be immune to Grave Shackles and Jolly Roger's Grave Bind.
Stun Immunity
Stun Immunity is a passive skill that causes your pirate to be immune to Stunning.
Game Note: After the effects of being stunned wear off, you will be briefly Immune to Stun Effects.