#mostly from memory

he uses respectful terms with the gods who care about that kind of thing: lord/uncle hades, lord zeus, even though he greeted his father first. he's more careless with hermes, but in a friendly, empathetic way. he's rude to ares but ares finds it funny. he made friends with apollo, and then impressed artemis, which probably made an even better impression on apollo. he followed through on his commitments to hades, both in the first book and after he was offered immortality, which made up for the whole beating the brakes off him after getting the achilles' curse. he trusted hestia with hope, which impressed and touched her. not sure about hephaestus, but he did fulfill a quest for him and he seemed to have a good impression of him. he's generally polite to hera i believe and carried her across the river in SoN, but i think he may have gotten mad at her after? not sure but i don't think he was crazy rude or anything. athena never liked him but he stayed polite, and i dont think he really interacted with demeter. he did a quest for persephone and got mad at her but she accepted her wrongdoing graceully i believe. dionysus and he have a semi-fond, semi-bitter relationship where they pretend they don't like each other i think by the end of the second series.

his father of course loves him and percy is polite to him, and poseidon has high enough regard for him to hear him out on a plan to defeat typhon, which he was right about, and that plan was enacted. and he's very kind to minor spirits, who are used to bad treatment from the gods because they have the power. like when the river nymph was scared he would use her water to clean the stables and he saw that and felt for her and chose to find another way even though he literally had no clue if that would even be possible.