The best starting poker hand in Omaha High is Ace-Ace-King-Queen double-suited.
Good starting poker hands in Omaha High contain: Suited aces, four-card connectors (10-J-Q-K), and two pairs as long as one is high.
If you have an A-A with two weak poker cards that do not add value to your hand, only play by raising if you are first-in from a late position, or if it has already been raises, no one else has called and you are in the last position. In the latter situation, you should make it three bets and attempt to run your opposition out of the pot.
Poker hands such as A-A-9-5 and A-A-9-4 shouldn't be played in any game except heads-up. One exception to this rule is the A-A-9-2 which could be played in some settings, but remember that A-A-9-3 is a weaker hand.
The closer your poker cards are to the A-A-2-3 double-suited hand, the better off you are. You can play these poker hands with aggression.
A-A-x-x hands, where x = high face cards, such as A-A-Q-J or A-A-Q-K, are better than the hands where x = a pair such as A-A-J-J or A-A-Q-Q..
One thing to keep in mind though is that Pot-Limit Omaha is the game most different in land-based poker compared to online poker rooms.
The online card rooms have buy-in limits that prevent you from playing the normally sensible way -- buying yourself a big stack of poker chips. They have capped buy-in amounts and thus require you to play small stack Pot-Limit Omaha (until you win your way to a big stack). In that way, AAxx is a much better hand online than in a casino, since any pot size reraise will often be over half your stack.