Stay aware of the nut hand possibilities. As the board develops, make sure that you always know what the 3 best hand possibilities are, and how that might change on the next card.
High pair with an over card is a good flop in Hold'em but not in Omaha. In this game you need to flop 2 pair, a set, or better.
Usually don't raise before the flop unless you are holding Aces or Kings and are in position to narrow the field. Another time to raise is when you are unraised on the button and have a strong hand. Try not to let the blinds play bad hands cheap.
Fold your Straight or Straight draw if that's all you have and you don't flop an unpaired rainbow. If you do get the right kind of flop, bet/raise to discourage the back door Flush draws.
Don't over value low pairs. A pair of 4's in your starting hand is only useful if it flops a set, but then a low set on the flop is not a very strong hand in Omaha.
Study your opponents, especially when you are not playing hands and can pay careful attention. Do they find more hands to play than they fold? Do they bluff? Can they be bluffed? Do they have any 'tells' (give away mannerisms) that disclose information about their hands etc.
Get caught bluffing once in a while. It is a way to vary your play and not be too predictable. You win pots that you don't deserve when your bluff works. You lose a few chips when it doesn't work but it will get you calls from weaker hands down the line when you are really strong and need the action.
Check the raisers chips. Players that are close to all-in often rush the betting just to get all their chips in a sink-or-swim last hand that doesn't merit a raise.