You should also think about
Reverse implied odds. Of course this is pretty hard to do
since OP didn't give stack sizes, so I'll assume medium stacks of at least 5 times the pot.
Villain is relatively unlikely to pay another cent with unimproved overcards, but relatively likely to call or raise with anything beating us. The somewhat hidden OESD helps the IO situation somewhat, but four to a straight on board makes it less likely Villain pays off.
If it's really even money whether we're best, then I can't see raising. Maybe taking a card off and hoping to stack Villain if he can't get rid of a big overpair.
Now, if
effective stacks are short then IO doesn't matter. We probably have ten clear outs, surely eight, and are even money to be leading. At that point I think it's a clear call though the only justification for raising would be to charge overcards to draw out on you.
As posited, without stack sizes, there's no single clear answer.
Everything in big-bet poker depends on stack sizes.