If nobody has a pair or better, then the highest card wins. If multiple people tie for the highest card, they look at the second highest, then the third highest etc. High card is also used to break ties when the high hands both have the same type of hand (pair, flush, straight, etc).
Omaha is a variant of Texas Hold'em Poker. Omaha is considered, by some, to be the hardest game of Poker to master. Of all of the different games of Poker, Omaha is for many the hardest to learn to play and the hardest to bluff in. It is played most often at fixed limits, like Texas Hold'em and pot limit.