Oooh, I love this and I have opinions about Byler!
Natural leaders, loyal to their friends, always organizing stuff, responsible for plans and... well, extremely proud, stubborn, harsh on new people and complicated with their own feelings. Wow, are we talking about Mike Wheeler or about Annabeth Chase? Couldn't tell the difference even if I tried.
Do I really need to say more than "Will is pretty much the fucking sun"? I do? Ok.
Artistic, deeply sensitive, loving and kind. Quiet personality, but fierce when needed. Also, canonically a music snob. We don't see much of Will shooting a gun in the series, but Apollo's children are usually good with weapons that require aim and we do see Will loading a shotgun when he was 11 years old with quite an ability, so...
About the rest of the party
I'm currently at work so I don't think I can elaborate as much, but:
Lucas - Ares/Poseidon's Cabin (couldn't decide): grounded (but also ready to fight if needed), independent thinking, protective, loyal and brave, but also stubborn.
Dustin - Hephaestus' Cabin: curious, problem-solver, goes to fucking science camp to build stuff.
Max - Ares' Cabin: I think she fits in this cabin more than Lucas because Max is not really grounded, she's explosive. She gets angry, pushes people away and if they try to get close she fights. But she also feels things deeply and she's extremely loyal to those she loves.
Eleven - Zeus' Cabin: cough cough terrible father cough cough. I'm not sure of the choice though. I mean, she's obviously the most powerful person in the group, super intense, has a definitive role in the story. But at the same time she's not actually a leader because she never had a choice on what to do (and when she does have a choice apparently we get season 5 episode 8). I don't know, not sure of this one.
Honorable mentions without ay elaboration
Erica - Aphrodite's (I KNOW you thought Athena, but I really believe Erica's all about Aphrodite's)