I learned omaha by playing freerolls
on Power Poker (Cake skin) a few years back. They were only $25s but there were some good players and alot of spew artists and the fields were small. I don't have any suggestions of a site to play Omaha freerolls on besides the daily Carbon one. Think it's at 6pm ET. Look around and I'm sure you'll find some other site that offers them.
Besides that, just read some strategy articles. There's a link at the top of the page. Search some threads here too. I haven't read too much strategy, just learned by playing mostly.
Omaha is probably not the game to play if you're trying to escape variance though.