Do you feel a little awkward reading Percy Jackson when they are doing 'god things'?

I don't see why anyone should feel awkward over such a petty thing. It's literature, nothing more. Just because a character in a book prays to a certain deity, doesn't mean that you have to agree with them. You can enjoy a good book without agreeing with certain things the characters do/say. In fact, I really doubt Rick Riordan himself prays to Greek gods and goddesses.