*rambling away from the hand in question here sorry!
I assume anything other than folding to a 3bet is turning our hand into a bluff
pre-flop in Omaha is a little less rigid than straight up "raise for value" "Raise as a bluff" it's pretty rare that you ever actually raise pre-flop "as a bluff" as it were in PLO you certainly raise hands that are "light" but this isn't the same in NL when you 3bet T6s as that is certainly a bluff 3bet (but you have some equity when called, but it's very unusual you could be callled and have anywhere near 40% equity) in PLO though you could 3bet someone from the btn with a hand like JT76ds and whereas in black and white definiton we are "bluffing" as in we don't really want him to 4bet us, and we certainly don't want to be all-in but we'll find that we'll be going to the flop with 40%+ equity a large % of the time, so IP that is pretty much a raise for "value." We might find ourselves even a little disappointed when they fold to our 3bet.
Other reasons for a 3bet like this would be that our hand plays better HU than multi-way, so if on average we have 25% 3way, but have 40%+ HU and the initative then that's another "value" element to our re-raise. We could pick a hand to 3bet pre-flop like 4567single, which prolly won't have as much equity, and therefore could be the closest thing to "turning our hand into a bluff" pre-flop given that it's a hand we could call with, and maybe in a vacuum actually isn't a profitable 3-bet but its good for our range over-all to have these low boards covered in 3bet pots as well, so that's kinda the same thing as 3betting 65s etc in NL...
More seriously, would the answer change if villain had say 8k? What range of hands would we expect to get him off?
If he had 8k, 50bb, then I think calling starts to show a little more merit, however I still don't like calling the 3bet with THIS hand with even 100bb stacks (I guess maybe if you think the player is espcially weak you could make an argument) Really I feel very strongly that doing anything other than folding to the 3bet is a decent mistake.
I think the intial open is OK, however the BB has a small stack and there are 3 shorter stacks in between you so maybe given the risk you're going to be playing a shallow pot with this hand post-flop folding from the offset is actually better - I wouldn't hate limping this hand even, given how well it plays multi-way.
What range of hands would we expect to get him off?
His actual hand i would have expected him to fold, however once he's 3bet off his stack he has closing in on half his chips in he is NEVER folding to the 4bet All-IN, so we have 0 fold equity here (imo) so in that case we need to make sure our hand has sufficient equity vs his range because we're gonna turn the cards over her most likely. If we have some (even a very small amount) of fold equity then the maths of situations like this become very forgiving, but you still need to have a hand that has enough equity 30%+ vs his legitimate 3betting range (hands that want to go all-in) and this hand just doesn't have that, despite actuallly finding ourselves a VERY small equity favorite in this hand we literally have run in to the absolute BOTTOM of his range, I don't think he can ever show us a hand here that has less equity vs our hand than this one does, and in my experience big broadway hands and hands with big pairs tend to be how people's "getting all-in" ranges tend to shape up away from AA with shorter stacks, so hands like AQQ5 etc which has us in a decent amount of trouble.