[Albert Moulton]

Fold preflop. If you really want to play, then reraise. But at 7% PFR his range is 88+,ATs+,KTs+,AQo+ which is a little better, on average, than AQo. For example, AQo vs 88+,ATs+,KTs+,AQo+ has about 43% equity preflop if you ran out all the cards.

Once you called preflop out of position in a multiway pot with AQo, I think you should donk the flop for $25 or so, and consider folding if you run into a big raise from behind you.

On the turn, I suspect you ran into TT. Here's my reasoning.

If his range is something like 88+,ATs+,KTs+,AQo+ (7.1% of all starting hands) for a PFR ...

KK-AA would have probably bet the flop.
*QQ might have slow played, so that's possible.
88-JJ might have checked the flop, but 88-99 and JJ would not have likely raised your turn bet.
AQ and KQs would have bet the flop.
*AcKc and AcJc might have checked the flop and raised the turn, but other AK/AJ hands that didn't cb would have folded the turn.
KJs and KTs would not have checked the flop and raised the turn.
*TT would make a lot of sense here.

So, you have AdQh vs TT,QQ,AcKc,AcJc giving you equity of about 23%. Given the size of the stacks and your bad position, I think folding to the turn raise is better than calling or pushing.