The characters and likeness are copyright of Valve Inc, and their likeness is under their copyright.
Not saying you CAN'T use them-- but if you do, Valve will MOST LIKELY come down on you and issue a cease-and-desist of some sort.
That being said, I don't think Mark Laidlaw has any copyrights on his characters, and presumably he won't be mad at fans trying to be creative, what he is apparently supportive of since he is upset with the way Valve is going. I'm not sure what the exact legality is but I am sure the characters will open a huge can of worms. You guys might want to play it safe-- but in any case good luck. Just wanted to let you know that just because this is a competition, that doesn't mean SOMEONE will be held accountable if Valve decides to try to shut this down.