Preflop
For me this would be a 3-bet or fold situation. Folding might seem tight, but he is opening from MP, and you are next to act with 4 more players left to act, who could each wake up with a hand. So if he was a tight or a particularly tough opponent, I would probably just let this one go. 3-betting can also be fine though. If you get 4-bet, its not like, AJ offsuit is a particularly tough fold. And if he call, you can try to take it away on the flop with a C-bet.
Flop
As played a standard call.
Turn
Now the situation already gets a bit dicy. AJ seems like such a pretty hand, but on a board like this, you are not beating anything, which is barreling for value. His worst offsuit AX is probably AJ, so same like yours, and if he has A2s-ATs he is not blasting on for value. So if you call now, you are clearly trying to catch a bluff, and you have put yourself in a situation, where your range is massively capped compared to his. He can have QQ-AA, AQ-AK, and you probably cant, because you just called preflop. So other than JTs and KQs AJ might be the best hand, you even have in your range. Which mean, that if you fold AJ, he can just bluff you to high heaven.
River
Now there is a 1-liner to a straight, but given what I just wrote above, I kind of think, you need to close your eyes and call him down. Is he still value betting two pair with that 1-liner out there? Thats certainly up for debate, and how often does he actually have a T in his hand? Probably not all that often, so I feel, this river bet could be a bit weighted towards bluffs, and that you should call in a 109$ tournament. If this was a micro tournament, my conclusion would be different, but from around 22$ and up you do see people find a lot more bluffs in situations like these. Like maybe he has A5 of hearts and decides to turn it into a bluff. But I would prefer to not be in this situation in the first place, and it could easily have been avoided by not cold calling preflop.