This is my opinion on how the different Percy Jackson characters would Draw/paint

Percy Jackson: I think he'd draw rather simple, more of a cartoonish style. And he wouldn't be very good at it, let's be honest. 

Annabeth Chase: She would try to always draw anatomically correct. But sometimes she allows herself to express her own style which she's still discovering

Grover Underwood: He doesn't really draw, but he would probably have a thing for landscapes

Nico di Angelo: Is actually pretty good at drawing, but god bless the poor soul to ever mention it. Except that one day, Will comes up to him and compliments him on a sketch and Nico just dies from blushing. 

Luke Castellan: I think that he'd keep scribbling out the faces so it looks like those phsycho drawing thinggies. 

 Clarisse La Rue: Uses the blood of her enemies

Jason Grace: He tries, he really does. But he's terrible. 

Piper McLean: She'd probably enjoy painting with a lot of wild colours, especially drawing flowers with thorns and berries. She'd also use rebellious patterns and colours that usually wouldn't fit together. 

Reyna Avila Ramirez-Arellano: Doesn't draw. 

Hazel Levesque: She'd have more of a soft, round style. Also often trying out new methods and patterns

Frank Zhang: Stickmen

Thalia: She'd literally draw on the corpses on her fellow treemates, are you crazy?! 

Leo Valdez: I think that he'd actually draw rather detailed, because he's an inventor and he needs things to be accurate. But at the same time he is the kind of guy who'd draw the sun into the corner of the sheet. 

Will Solace: A lot of bright, warm colours. Is pretty good at drawing nature since he can identify different healing plants and things like that. Smiley faces on everything. 

 Rachel Elizabeth Dare: is literally angry Bob Ross 

Zoë Nightshade: Likes to draw, but would never admit it. 

Bianca di Angelo: Rather dark colours she then decorates with fine silver and gold details

The Stoll brothers: Throw a colour-grenade at the canvas and see what happens

Calypso: Lots of pastell colours. She'd probably start with some lines and then draw what she sees. 

Apollo: Self portraits

Did I forget anyone?