Actually, i've tested APHEELSICK and TT's Poison just now and here's how it works:
Poison stacks with itself, and negates a total ammount of health that would be regenerated untill you explore a set ammount of tiles (and it notifies you about how many tiles you have left to explore before the monster starts regenerating). It doens't "break" if you attack something else anymore, and for that I'm very, very glad.
APHEELSICK adds 10 poison points per level. It stack with itself.
TT poison adds 10 stacks (fixed, not per level) of poison with every attack. It's abysmal compared to APHEELSICK. It costs 35 piety, and increeses by 10 piety for each hit of it you take. It also means that to use it effectively you need to be out of TT, and it especially means you can't prep TT with it in mind. Essentialy it's like applying a lvl 1 caster APHEELSICK to every attack you make. I feel it got hit too hard this time, and might need to be buffed, either by making it a fixed 25 piety per boon, or upping the ammount of poisonous attack.
How the venom dagger works I have no clue.