AQ

Calling to the c/r otf seems standard to me.

I'd probably bet turn, although I am not sure thi is theoretically correct.
V at this point may slow play a boat, but he can also just be hoping to get a free card with a FD.
If he c/r again, then we are admittedly in a tough spot.

As played, otr in theory you are deep enough to raise/fold (~150), targeting a worse AX, but it really depends on how light V is willing to call.

I'm calling the flop. Betting the turn.

As played just calling the river. 78 got there as well as the flush. Don't think there's value in raising.

Preflop seems small, but depends on how your 2/5 game plays. I would call the river.

Let's try and consider a range for your typical loose-passive low stakes fish:

Called a 4x open preflop. But people HATE folding their blinds and probably aren't really thinking about the limper behind. I'd say it's probably not total crap but very wide here for sure.

OTF:

kind of important which suits are which but from the turn description the 9 & 6 match. I like the bet, and the xr means what? I'd say it's flush draws, two pair, sets and maybe 78. very very rarely something like AK/AJ I guess.

OTT:

Checks when another A hits? If he has a set he just boated up, if he had two pair he probably boated up. If he has the nut flush draw he just made trips. Seems unlikely a boat or trips checks here, so that tells me he has a flush draw less than the nut flush, 96 and 78 still.

Personally, once he checks I might bet 1/2 pot again to recap his range. checking behind is probably fine but it does limit your choices on the river.

OTR:

$50 into $210. You have $400 back.

This looks like a straight or lower flush. Nut flush would go bigger and would have bet the turn picking up trips. 78 might have checked the turn getting scared of the Ace. Don't think 96 would bet here if they checked the turn.

All the people saying to call are strange to me. What bluffs xr flop, x turn, bet 1/4 pot on river?

So the question is, do you think there's an amount you can bet that gets a non nut flush to fold? I think your biggest obstacle here is the check on the turn. Hard to credibly represent a boat or nut flush(which would have hit trips on the turn and not bet when checked to?).

We call, we'll get shown a baby flush at worse. We raise small, I'd be surprised if they fold. We raise big, I'm still not sure they would fold.

So think how much would we raise with a boat(we slowplayed I guess?) to get a non nut flush to call? I think they may call up to $150 or so. Which means if I'm raising, I'm going $250 or $300 at least. Though honestly I'm probably just folding since once we check the turn our credibility is shot.

People do strange things you really are folding to $50 into $210? He doesn't have an ace or a weird bluff 20% of the time?

Could be raising flop to "see wheres he at" with some random ace, checking turn to either trap or because he's still not confident you don't have an Ace with a better kicker. River after flush comes in he figures he can only get paid with a small bet from worse.

Bluffs are a little harder to imagine but I think you still need to factor in that they could be happening a few % of the time.

A weird bluff is always possible, but would he really check trip aces on the turn? Scared of monsters under the bed?

I know the price is really good, a call can't be the worse decision but it's hard to figure out what it could be that we beat.

I think your range is so face up as AX when you call the x/r that checking back turn is a crime. I could see bombing turn depending on stacks. River is whatever..call I guess.