With 20/20 hind site checking the flop was what you should of done. However without the hind site your play may not have been the best ( I can't say for sure since it is almost impossible to second guess a player on the scene, since I could not see what you saw). Considering your position, that you raised preflop and the quality of your hand I think a follow up bet was called for.
With a follow up bet many good things happen for the player with AK, you thin out the field leaving dead money in the pot which is always a good thing. Most players will lay down gut shot straights, and some will laydown small pairs (like 3's and 4's(Although with your particular board and loose players it is not as likely they will laydown)) and almost all players will lay down hopeless hands that have no chance outside of making a pair, to win a pot, you don't want to give them that chance to make a pair. You also maintain control of the pot which has a lot of benefits, like being able to set up a good bluff or driving out hands that do not beat you yet. It also gives you a better handle on the holdings of the other players, giving you vital information about how you should proceed. Doing a follow up bet with AK on the flop, even when you hit blanks, is not a bluff, it is more akin to a semi bluff, where you may take down the pot right there, or you may make a hand that takes the pot at showdown.
I raised to kick as many opponents out as I can (is this a correct move?)
One should really not care how many people call when AK is held. The hand plays well short handed and is more profitable with more players seeing a flop, although more subject to a higher SD. It really depends on how your comfortable playing the hand. For example you might be more comfortable with fewer players in a hand or like to go after the big pots with a little more risk.
So what's a good strategy in this case? In short, don't bluff.
There is no default best strategy here. It all depends on what seems to be going on with the other players. There are definitely times when you should just take the free card on the turn, other times you should follow up with a bet. You can really only make a good educated decision about what to do on the day.
So my question: even if a strong hand like AK in such situation can't win against poor players, then what's a good strategy to play against them?
The 2nd best strategy is to raise preflop and follow up with a bet on the flop. The best strategy is to raise pre flop, then take in all the information you can to determine what to do on the flop. You had a good handle on the players that were in the hand. It is not impossible that a follow up bet would of taken the little pairs off the hand. However if you had no reason to believe nobody had a pocket pair, a bet was called for, if you had some good reason to believe they had pairs and you did not want to risk the price (if indeed they could be bought) of getting them to laydown, your play was great.
Your contention that AK "can't win against poor players" is very much an incorrect conclusion. AK plays much better against weak players who incorrectly play their hands then against strong players who may be able to lay down loosing hands.