We are playing 8 handed.
Villian 80Bb opens cut off.
He has been playing fairly aggressive.
Hero 22Bb with AJo
There is 10% ante.
Currently 50 left/250
Payout starts from 40th place.

What should hero do here?

Depends on our position at the table. If we're BB I think shoving is definitely profitable. SB is also probably a profitable shove, but certainly bears some risk. I think flatting in position is decent enough from the btn considering we're in position and have a decent amount of chips to play post flop. If villain is aggressive then we can perhaps double up playing post flop catching bluffs on a variety of runouts. You have to remember, if villain is a smart aggressive player then he knows the closer to the bubble the more he can open wide and steal. Playing a pot post flop is fine with our stack in position.

Jamming btn for 22 bbs feels pretty bad considering we have two players behind who will always jam dominating/flipping with us.

Did he min? Prolly jamming regardless

Yeah, you left out a couple crucial details - your position, and the stack sizes of the other two players remaining in the pot.

They continue typically with tight ranges. Yes, we do badly when the do get it in generally, but it happens rarely.

OP, this type of problem can be modelled effectively using ICMizer or Hold'em resources.