Pre-flop: This isn't even a close pot. I'm snap-folding this as soon as the 3-bet comes in. The reasoning is we're OOP against 2 of the 3 players, we're not last to act (the CO could easily 4-bet), we don't have any reads on the players, we're usually dominated by at least one player, if we flop a draw, it's rarely going to be to the nuts (a consideration in a 4-way pot), we only have $0.02 committed (so we're not priced in at all). That's 'Why not to play in 6 short reasons'. It's true that the CO looks fishy, but we don't know what type of fish. He could very easily be a passive fish that only 3-bet big hands in which case this nugget of information makes this an even worse call. I think the lesson here is that you need a combination of factors in your favour to unorthodox plays, not just one. You've got to weigh up the pro's and con's of the situation.
As played, the SB is probably going to be squeezing quite wide, so we'll give him a range of 88+, AKo, A2s+ and KQs. Since he's squeezing two players in LP, he's going to have a wider range than a standard squeeze, with more bluffs in. Anyhow, this is probably as wide as he possibly goes here.
The BTN calls and since he's IP and getting a good price (from your call) he's probably calling most of his range. Since I wouldn't expect his calling range to be too wide from the COs initial raise (he 3-bets quite a lot I think), we have to adjust his range to include only hands that both call the initial raise from the CO, and call a squeeze from the SB. I put this together: 77-JJ, AQo, ATs-AQs, KTs, QJs, JTs, 65s.
Flop: This is a pretty great flop for us. A strong flush draw, a double gutshot and a straight flush gutshot. We should know instantly that we have at least 15 outs, possibly more if we're not against an A (although we often are). This gives us about a 54% chance to hit a diamond, K or 9 by the river. Since we're a favourite to just about any hand, we should play this fast and look to semi-bluff here.
The SB c-bets into 2 players. That's pretty strong and means he has a minimum of Ax here. That's the majority of his range but he can also have sets (88,JJ and AA), AJ. Raising is good here, but I just shove to get maximum fold equity (winning this without any risk is better than flipping for stacks if we can). The BTN shipping it behind you is super-strong, but it also gives you way better odds
on your draw, so it's a good thing for you. The action behind him is so strong, I'd expect him to have either AJ, 88 or JJ every time here.
Once the SB moves all-in we can take weak aces out of his range, he's probably got a minimum of AK here (and often he'll have better). Obviously we call.
Now, obviously we hit our hand, which was nice and we nearly treble up. We should note that both players overvalued weak hands. The BTN really should have folded J8 with the action behind him, and I would sure as hell have folded AK with two players effectively going all-in behind me if I were the squeezer.
Post-flop this hand plays itself, pre-flop we simply need to fold.