On the button if limped to me by a couple of people, I might be tempted to call this preflop and have a look since we would have nice pot odds and position. Second to act, this is always a fold, since nothing tells
us we're not facing a raise later and we'll have average position. I want to close the action with such a drawing hand since I want to check myself a free card on the flop, draw to proper odds or trap in dead money if I flop something good or huge (FH for example).
Flop I tend to say fold a lot of the time since we are holding middle pair no kicker and runner-runner to a straight. But the pot is big and we aren't likely to get raised, so peeling one off is probably okay, but with subsequent streets, we have to realize that our equity will go down and not up due to overcards, two pairs hitting on us if it goes multiway and our hand doesn't fill or improve. On the other hand, our effective odds are pretty low: the pot is lying us around 8:1 now, but we have to put a BB on the turn the times we don't hit, meaning we invest 1.5BB to win 7.125BB (on the river assuming all opponents still bet and call) and the odds are even lower if we get raised at any point. Since our odds of winning with the measley 7's are very low against four players, we need to fill in order for our play to pay off. We'd need 20+% equity to make this play +EV in the long run and I doubt we have it multiway. I don't see a raise here working, what with the decent pot odds opponent would still be getting out of the bloated pot. Maybe I'm a nit, but I fold.
Turn I'd also play is passive and only call since we now have outs for the straight, two pairs, and the pot is large. But, I would've preferred a flop fold.
River, you need to bet this since the raiser won't bet it if it is checked to him. The 8 is scary even fo a set, so bet it yourself. You'll never get a c/r here.