I think it's generally agreed that Percy is a clear ESFP and Annabeth an INTJ. But I'm not sure about Grover being a J. My impression of him was ISFP - Fi, because his values factor in to all the things he does - he wants to save the environment and follow in his family's footsteps in trying to find Pan. Se, since he's in tune with nature and pretty observant. I could be wrong, though!
As for other characters:

Nico - INFP
Zoe Nightshade - ISTJ
Thalia - ISTP?
Rachel - I get an ENFP vibe from her
Clarisse LaRue - ESTJ
Connor and Travis Stoll - ENTP