[asterion]

Well, as I said, the main strategy (such as it is) is all in the betting. Remember, you generally only get once chance per hand to bet, so you need to get it right before the hand is dealt. You want to know the basic strategy, at the very least, for the rules the tournament is played under. They are, if I remember correctly for Elimination Blackjack:

Six-deck shoe
House hits on soft 17
Resplit to four hands (no resplit on aces)
Late surrender
Double after split
Only one card to split aces

Having some idea of when to make unconventional plays (splitting 10s, doubling-down on 12, and such) helps as well. But most important is an understanding of betting strategy. I suggest getting a book (I have no suggestions) and reading it. But for an example:

Say it's an elimination round and you are matched with one other guy for the short stack. If you're lucky enough to bet after him, you can adjust your betting. You have three options then: match him and hope you win and he loses, go much bigger than him (if possible) and hope you win and he loses, or go much smaller than him and hope he loses and you don't care about your outcome. The same holds true, to a lesser degree, with the intermediate hands. If you're a big stack, you probably want to match other bets or maybe go small. If you're a short stack, you'll need to bet more aggressively.

Seriously, though, get a book and read it. I promise that most of the ideas will carry over to elimination blackjack.