[Pov]

I think the problem most people run into with "big cards" that miss is they don't realize what they've got is a drawing hand. If I give you QJs and a board I'll bet you'd have a good idea what to do with it because you're comfortable (probably) with drawing hands. When up against one or possibly two opponents there is a reasonable chance you actually hold the best hand, but against several opponents you are almost certainly drawing.

Well your AK missed and as others have stated with 4 opponents it is virtually certain that someone else has at least a pair of something so you are behind and drawing. The only difference is you were the pre-flop raiser so you've given away your hand to some extent, but you could also pose as holding a high pair. In a low limit game against 4 opponents posing as the high pair is unlikely to get you anywhere since anyone that matched the board is probably coming along at least until an Ace hits the board.

Armed with this information what should you do in the various situations that might arise. I'll second AKQJ10's estimation of 5 outs as that's about where I would put myself in your situation. There are too many AT's, KT's, A6s's etc. to count your overcards as 6 outs and I'm going to make the assumption you do in fact have a backdoor flush draw to get you up to 5. That's a pretty weak draw, but because of all your callers the pot already contains 10 bets or more. So what might happen:

It is bet and raised in front of you - easy fold

It is bet in front of you - we already know we are getting odds to see the turn so the question is between calling or raising. If there are no callers between you and the bettor, a raise is very tempting to attempt to fold out the field and to try for a free card. I would mostly be making the play for the free card here. If you don't think those things are very likely, I see nothing wrong with just calling and trying to get to the turn as cheaply as possible.

It is checked to you - I think this is a tough one and you really need to have been paying attention to you opponents. Your bet will be offering at least 11:1 to the field. If I was first to act with 4 players after me I would almost never bet here, though I might check-raise if the last player bet and he was the type to bet just because it was checked to him. If I was one of the later players I would be more inclined to bet for the free card potential on the turn. When you say "called down by two others" it is unclear to me whether they were behind you or in the blinds and that would affect my play.

So let's assume there was a bet from somewhere and you made it to the turn 3-handed. That means there is now something like 6-7 big bets in the pot now. If you pick up your flush draw you've got an easy time of it since you'll have more than enough outs to see the river. If you don't you're very likely going to need to fold here unimproved. This is why I would have been inclined to go for a free card on the flop *if I thought it had a decent chance of working* since I know my hand can't take much of any heat here on the turn if it doesn't hit.

I think the toughest decision is if a J or Q hits on the turn. Your straight outs are strong, but it further clouds your overcard outs since you're now much more likely to be up against two pair or a hand that will be two pair or a straight when you hit your top pair. I think in this situation you just have to go with your gut and what you know about your opponents and the types of hands they might be holding.

This may seem like a lot to think about in the heat of battle, but it comes up over and over again so you should really spend some time going over these possible scenarios and try be ready for them. If you can master these types of situations you'll be in good shape to be a consistent winner.