Omaha is highly situational. In hold’em, you can get pocket aces ten times in a row and it may usually hold up even if your hand doesn’t improve on the flop, turn or, river. In Omaha, you can get a strong double suited AKAK and never win a pot if the flop always comes six high.
Look at Omaha as shifting the action one street later. Pre-flop, you can play nearly any reasonable cards to see a flop, the flop is when you commit more to a hand, the turn defines your hand, and of course, the river finishes a hand (one way or another)
Because of this shift, you should play most of your good hands on good flops straight forward both to get maximum value and to protect your hand. In Omaha, like any poker game, if you think you have the best hand, your goal is to make your opponent make a mistake. Giving them incorrect odds to draw out on you is just that, and can be achieved by a pot-sized bet, especially if you follow that up with a pot-sized bet on the turn if a blank comes down. You’ll force them into a second opportunity to make a mistake, and if they draw out, you’ve done all you can.
For this reason, you need to know when to move hard on a flop and when to wait. Most of the confrontations in Omaha are between a strong made hand (top set or the nut straight) against another draw or draws. Redraws and wraps are powerful, and if you’re fortunate enough to hit a flop with both a straight and a flush draw, you’ll usually want to get all your money in however you can.
If the opponent has a hand, they’ll usually come along with you on the flop, so make them pay if you think you’re best.
Position isn’t as big of a factor as in hold’em. But if you watch the action, position can be used as a bluffing opportunity. If there doesn’t seem to be much action, a hand like two-pair can usually bet out thinking the hand is good. A late position player may call with the intention of bluffing at a turn card that looks like it hit a draw and try to chase out the opponent if they then check. They may also be trapping, so know your player, and you may even try that move yourself in early position.
Additionally, later position allows you to read the opponents’ hands better. If there are three flush cards on a board and you have just the ace of that suit, a bet and a raise tells you that the raiser probably has the flush and wants to know where the ace is. No, you don’t have the flush and can’t improve to make it, but if you call (hopefully with some kind of two pair/set draw to pair the board so you aren’t totally naked with the “dry ace”) and they put in a smallish bet or check on the river, you might steal the pot by blasting them out with a pot-sized bet, representing the ace high flush that you know they don’t have.
The best strategy to progress to expert mode is simple: just as in any poker game, know the odds, know the players. Odds calculation is standard, as most players at this level will know the basics from hold’em (just adjust for the additional known holecards). But since so many players play nearly every hand in Omaha, be prepared for odd things to happen. That way if you have a set of kings on a K356 board, you’ll know if the player checkraising you is capable of playing with a 2-4 or 4-7. Some players merely represent this hand, others play it regularly for just such an opportunity (which is a good way to mix up play if used judiciously).
Omaha creates huge pots, since often there are multiple players seeing a flop, a couple hanging around to see if the turn completes their draws, and thus, a lot of dead money if you hit the nuts. It’s also a game of protecting made hands and big draws. You may, then, think of increasing your bankroll requirements to account for additional volatility. Flopping a set with a flush draw is a nice place to be, and if you can get your money in the middle, great. But your hand isn’t always going to hit by the river, so be prepared to come up empty from time to time on the big draws while a tiny straight rakes in the money. If you can handle those swings both financially and emotionally, and play with a sound mind towards the possibilities, you should be able to succeed at Omaha.