One of the most important things in Omaha, that you need to learn - is that all forms of Omaha are built on the value of starting hands. That is the value of the starting hand is usually predominant in comparison with the position, which is much less important in Omaha than in limit or pot-limit Texas Hold'em.
You should always start with four cards, which are somehow linked. On the flop, you must have either the best possible combination or the possibility to form such one in order to continue play with your hand. If you have a drawing hand, then your possible combination must win the pot when you make it. If you're making flush, it must be nuts flush. If you make straight, make nuts straight. In other words, you have to make only the best combination.
Best possible combination with backup variant
This principle, which is important in cash games and that is very important in the tournament: If you have drawing hand, then you should have a backup variant to your drawing combination – subsidiary drawing combination. For example, in Omaha Hi, you can form a top or second set on the flop, plus possible nuts flush or nuts straight. With your backup variant (or variants) in your hand it is much more likely to win than if you had just set.
Now let's say that you play in a tournament in pot-limit Omaha and formed a set on the flop, and in your hand it is not possible to form a flush or straight (no backup). If on the fourth street a card to a straight or flush is opened, than will you call a big bet to try to get a pair on fifth street? You must be extremely cautious in such situations in tournaments, when it is so important to have a backup possible combination.
Pot-Limit Omaha is the only one ever invented game in which you can form nuts on the flop, and you'll have to throw it. Suppose you have formed nuts straight on the flop and bet. If there are two suited cards on board and more than one player have called you, then it is possible that someone has set, and another, most likely, possible nuts flush, and you'll lose in this round.
Here lies the difference between pot-limit and limit Omaha. In limit Omaha, where it cost only one bet, you have to play your hand and hope that no one will beat you. But in pot-limit Omaha you should put all your money in the pot and pray that your hand will be the best at showdown, so often the best thing you can do is to muck your hand. All the best tournament players did this a hundred thousand times.
And what about the possible nuts flush in pot-limit Omaha without backup variants? For a lot of money, it would be a bad bet, especially heads up. But if pot is big, everything can be different. Sometimes in pot can be a lot of money before the flop, and you receive call from three or four players. In this case, if you have four-card nuts flush on the flop, and somebody made a bet before you, and several of players have already called, most likely, you really very want to continue. But you should not be the first one who starts betting with such hand - you first have to check everything, because everything you have is a possible combination.
Now you have same situation in the cash game. Here you need to call bet, when pot is great, and if you do not mind getting some more money out of pocket in case of losing. But in a tournament (except cases when you have a lot of chips and you're just trying to grab more) you just can not call, because if you lose, you'll leave tournament.
You can play a much greater number of hands after the flop in limit Omaha than in pot-limit. That's the difference between them: you can use the combination of a limit game, which you would have never used in pot-limit game, or tournament. But in both situations it is always good to have a backup variant.