Ugh @ that hand.
Firstly, I'm kicking myself for not thinning the field pre.
My excuses would be (see, I'm good with excuses) that nobody will fold in these sort of games, so I'm just inflating the pot oop, & in truth, my aces are pretty bad aces. I think, though, that better players than me pot it pre, & fire out on that flop, & they soon know the score, & have no more tricky decisions.
You have the third nuts, & we are only behind to

or

It is 4 card, not 5 or 6 card, so we'd be a bit unlucky to walk into either, but both are perfectly possible.
So, wwid now, on the river?
Well I'm over a grand ahead on the evening (I'm assuming, by stack sizes), so I probably do the usual wimpish thing & check call. Here are what I consider are my potential options.....
If I check, then it goes bet-raise, I sigh fold.
If I check & it goes bet-call, I call.
If I'm feeling particularly brave, I bet around half the pot, & fold if it goes (behind me) raise-raise, or call-raise.
I probably do the latter, (bet out) as the cheapest way out.
The worry would be that kiddo with Q-K, Q-A (unlikely) or some other shite underhouse (he can even have Q-2, daft as it sounds, danglers are so powerful, or he COULD even have Jx diamonds for a regular nut flush), he MIGHT think he has the abso nuts, & pot it or re-pot it, & if he does, then we have levelled ourself & it's hard for me to call then, & for that reason, I'd bimble about just check-calling.
Guess it's player dependant, too. Down at Luton in the DC, I would know excactly who would do what. If Gino potted it, I'm running a mile, if Chandra potted, I'm calling quickly.
There you go, Omaha as played by mega-nits.
FFS don't show LilDave or Greeky this.