Hand Rankings are exactly the same in Omaha as in Texas Hold-em, Only difference is in order to win with any hand, you have to use 2 cards from the 4 you are dealt, So if there were 4 Spades on the Table and you are holding the Ace of Spades, You have not made a flush unless you are holding a 2nd card in the same suit. Likewise with a Full house you must use 2 from your dealt cards so if the board has 2 pair and you are holding 1 of the cards involved it is not considered a Full house because the 2nd card you play, breaks up the other pair on the table unless it matches one of the other 2 cards on the table.
Can be very confusing if you have played Texas Hold-em all your life and try Omaha for the first time.
Now Short deck Texas Hold-em does change the Rankings slightly because you are only Playing with 7 cards from each suit, so in order to make a Flush in Short Deck you need 5 cards from the possible 7, but with a full house you need 5 cards from a possible 8, Therefore a Flush in Short Deck beats a Full House (more confusion) and if that does not confuse you enough, try some of the other Poker variations like Razz or Horse!