If the 4 move checkmate issue has only recently been solved at your high school, then I suggest doing a couple hours tactics and you should have no problems destroying all the patzers.
Good Chess Openings for a Scholastic tournament?

you could try the French as black. (e4-e6-d4-d5) or, you could try the Queens gambit as white. (d4-d5-c4)
Good luck! Hope this was helpful

Try the tactics trainer on chesstempo.com. It will help quite a bit.
As far as openings, people at your school aren't going to be playing theoretical openings, so just go with 1. e4 and follow general principles. Also hit the king's bishop pawn (f7/f2), quite a few people will probably miss mates on those squares.

That's an example of what I mean by "Hit the king's bishop pawn". You can get a checkmate by attacking that pawn twice with either bishop and queen or knight and queen. If you have knight and bishop attacking f7, take with the knight, forking the queen and rook.

What Ora posted is a Colle. I'd recommend a London (The only difference is that the white dark-square bishop is active and outside the pawn chains). The knight wants to get itself to d5.

Caro-Kann as Black. People who play 1 e4 as White tend to be aggressive. Aggressiveness rarely works against the Caro-Kann (though there are a few lines that can become sharp), so your opponent will just be "biting on granite" as Nimzo would say.

The OP has an 838 rating on here, and is pretty sure he's the class of this field.
If there's anything remotely correct about this, his opponents aren't playing e4 because they're aggressive, attacking players. They're just hoping they didn't just play a move that will cost them their queen, and struggling to understand what "castling" is.
The best opening here is something like: develop your pieces, get castled, and check every move to see if you're about to lose a piece. Anything much deeper than that is just going to cause chaos and confusion.

Against low level amateurs the italian game will usually give you a crushing attack when playing white. Try the Evan's Gambit if black replies 3...Bc5 or go for the Fried Liver attack in the event of 3...Nf6, they will give you an enjoyable attacking game, not to mention that other players will look at you with owe after moves suchs as, say, 6. Nxf7 (signaling the Fried Liver).
As black you could try a solid opening not widely known to begining players, such as the French or the Alekhine, according to your taste.
Edit - I just saw Artch's post above, and these are good points. I wouldn't advice any player bellow the 1000 mark to get concerned about opening theory (although the two videos I linked to may still be interesting for you in that they teach tactics).

Could you maybe elaborate on "couple hour tactics"? I'm new to these kind of terms.
Tactics trainer and puzzle books would be fine, considering the level of the opponent.

Play a gambit or just use this "system" against typical beginner h5 rh6 and so on openings. 1. E4 2. D4 3. Nf3 4. Nc3 5. Bc4 6. Bf4 7. 0-0

Try the kings gambit its even more amazing to those playing because you often sac a piece or two aswell
The London and Colle look very similar to the stonewall attack. Would that work as well, as it develops my pieces and is relatively safe?

No. At this level, openings that sacrifice pawns - or pieces! - are a losing option because it is far more likely that the player doesn't have the tactical skill to handle the resulting positions. In that case, he's given away material for nothing. Better to wait for the opposition to "sacrifice" pieces and just concentrate on making fewer mistakes and winning won positions; for instance, if you don't know how to win an ending of K+P+P v K then you need to revise...
My highschool is having a chess tournament and I feel like I have a decent shot at winning it. What are some great opening moves that abuse mistakes made by some not so knowledgable players. Also, almost eveyone in the tourny knows the four move checkmate and how to counter it. Any help would be greatly appreciated.