How would you play AK offsuit on a very loose table where 4-5 players would call a 3 bet preflop raise?
I would put in a small raise preflop to help manage the pot size to be small later - small enough so that my later large bet has a chance of pushing them off so I can win the hand. I might just call if it's already looking to be 5 or 6-handed, but if I'm early, I put in a small raise.
Making a large bet at this table is foolish - AKo does NOT play well against a large field.
What do you do if you have 3-4 callers and completely miss the flop?
It's not whether I missed the flop, it's whether they missed the flop. If the flopped shows no possible draws, I may make a large bet (large relative to the pot - which is hard if you bet heavily pre-flop.)
If the slop shows draws, I check and try to judge the action to decide on a call.
If I didn't bet the flop and the turn shows blank (no draws improve), that's the time I prefer to put in a large bet to take down the pot.
The river is the last story... you really need to get to know your opponents. Sometime, a scare card will induce one of them to bluff, but calling them with naked AKo can be risky, because although they may have missed their straight/flush, they might have scored middle pair. It's much easier to call an induced bluff if you actually scored an ace or king on the board. If not, you do want to call down sometimes - but very rarely. Only when your odds of being right are best - like when they've very likely been chasing a straight, and the river puts a back-door flush on the board, and they make a bet right after someone points out that a flush is possible, and they are the type that likes to make blind stabs on the river...
You'll lose many of these, but you'll win a few. As long as you don't call off your money on the really big-bet ones, it will be a profitable play - and you'll plant a seed in their minds that you're not so easily bluffed, reducing how often they'll try it against you in the future.