River all-in is somewhat alright there. I assume you don't have information, we can fold turn already, AJ ott is type of hand which can't improve almost ever and can't face agression too.
However folding turn is tight, river is quite good card to be bluffcatching or shoving. There is huge chance villain don't bet straight there(and KQ) and only valubets QJ and AQ and 44(but they don't raise turn much) and bluffs JT, T9 or something random.

I wouldn't fold the turn since we can dominate some part of his value betting range (QJ).
But I would fold the river, paradoxically because we can't dominate any part of his value betting range. And also I doubt that he can find enough bluffs on the river to justify a call, especially when he called the flop with one player behind=he had something. That being said since I don't have enough confidence that people are turning pairs into a bluff, I can say that I don't see enough bluffs from villain to justify a river call.

I just wonder.. against a fishy player, what about shoving the turn? To get value from worse hands (maybe some random worse twopairs or rarely from pair+draw or so).

Any info on villain?

I like jam, you block AQ and JJ. Also AA and AQ make perfect sense for you to have. So his straight or 44 isn't happy.