A bit over 1 PSB left going into turn. Villain is a 41/18 fish.
We block the NFD and the nut straight draw.

GTECH G2 (Boss) - C$0.30 PL Hi (6 max) - Omaha Hi - 5 players
Hand converted by PokerTracker 4

BTN: 80.17 BB (VPIP: 42.17, PFR: 19.04, 3Bet Preflop: 6.92, Hands: 417)
SB: 297.13 BB (VPIP: 47.96, PFR: 29.22, 3Bet Preflop: 12.74, Hands: 3,356)
BB: 132.4 BB (VPIP: 82.08, PFR: 13.29, 3Bet Preflop: 2.89, Hands: 1,559)
UTG: 125.97 BB (VPIP: 72.02, PFR: 5.09, 3Bet Preflop: 0.00, Hands: 636)
Hero (CO): 96.83 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has J A J 2

fold, Hero calls 1 BB, BTN raises to 4.5 BB, fold, BB calls 3.5 BB, Hero calls 3.5 BB

Flop: (14 BB, 3 players) K J 8
BB checks, Hero bets 14 BB, BTN calls 14 BB, fold

Turn: (42 BB, 2 players) Q

Your line pre is novel. I enjoy a nice open limp from time to time, although I suspect with a hand this bereft of potential a muck might be better. Presumably you were looking to get into a pot with the BB; perhaps we could limp fold to BTN's pot raise as well.

There is a decent chance that villain hit the straight. In that case we are in somewhat bad shape, maybe 25%-30% equity. On the other hand he might not have hit the straight, in which case we should be a significant favourite. How likely are both cases?

Villain could have diamonds, probably nut or w/ something else like Kxxx or QT. He could also have two pair, probably not KJ which would just raise. Probably a set would raise this super wet board on the flop. T9 itself won't be calling, but T9 + something extra would.

I dunno but I'd probably bet it. **** it, yolo. If he did hit it make sure to curse at your monitor.

Way ahead way behind situation. Default is to x/decide, betting doesn't accomplish much imo.

How big of a bet would you call? I wouldn't call >2/3 psb tbh, would you? Do you think calling 1/2 psb and bluffing diamond river with our blocker is correct? When we'd call a 2/3 psb we definitely can't do so + our odds get too bad so that's why I set the threshold to this sizing.
Really not sure about diamond river when he's betting around 1/2 pot, cause this could easily be a sizing with a flushdraw + 2P/Set/etc. We definitely don't have to since against this sizing we get the nice odds to call our set.

So in this spot where a straight may have gotten there, you check/decide and potentially give the FD a free card rather than bet for protection and potentially value town ourselves? Similar spots come up quite often (possibly str8 completed, FD on board, we have set) and I've always been barreling but I think it may be a big leak of mine.

It's just gross cause it actually sucks when we're raised OTT. Yes we want to bet for value/ protection against his flush draws, 2p combos etc. but the average expectation on this turn is that he's going to have a lot of straights. Of course there's other spots where some straights complete on turns but you're happy to barrel with your value hands because it isn't a really easy straight draw to complete, whereas on this board the Q is one of the nut worst cards because it completes a few.

Stacks are also awkward in that if we bet turn we're committed if villain jams so I'm not happy betting unless villain is capable of jamming this turn wide, which I'm not even sure he'll put it in with worse value or like Pair+fd+gutter or worse.