This is an obvious fold.

Hero has an OESD, but no pair, and is clearly behind even Ax bluffs from Villain. Villain is betting like he has Qx at minimum, and there's no reason to think a J OTR is going to help Hero's hand. Given there's every reason to think an 88/8 has at least a pair +FD in this spot, Hero can't be too happy with any clubs OTR.

So Hero can probably win with a 9 or an A or a maybe a K, of which there are 11 total.

Note that a K OTR is going to slow Villain down if he has a pair of Queens and a missed FD, so the King might have negative implied odds, meaning it will scare Villain into NOT paying off. Not to mention, that Villain could easily have 2 pair or better already, so the K is bad when Villain DOES put more chips in. Also note that any club OTR is going to slow Hero down, even if Hero makes a straight.

So those 11 outs go down to 6.

With only 6 clean outs, Hero has ~13% chance to "suck out", which is roughly 8:1 against, and so Hero needs 6 more bets from Villain + the difference in the overbet, or 6*$0.38 + $0.07 = $2.35. That's more than Hero can afford (and we haven't considered rake, yet), so there is absolutely no way to make a call a +EV play.

Unless there's fold equity, which I seriously doubt.

Did you follow the reasoning here?