Naruto is the son of both Chaos and Amaterasu

he is the Shinto god of beasts, divination, Chakra, bloodlines, angels, fallen angels, reapers, Destruction, love, day, Annoyance, Peace, Elements, Pranks, Sun, Universe, Order, Darkness, death, loop holes, family, bonds, yokai, under world, magic, talisnens, seals, homo pregnancy, war, weapons, heavens, earth, and the Shinto god of Shinto gods.

While he's the Greek/Roman primordial of Hatred, Space, Time, Stars, moon, night, demons, Elements, Bravery, Respect, Loyalty, Universe, Creation, Chaos, magic, Cosmos, Light, mentality, homo love, monster, nature, land, sea, sky, and the Primordial of all primordials.

Also he is heir to the title Creator of the Universe. Also heir to the Shinto throne as ruler of the Shinto Universe. and master of the fates

paring

naruto
x
Percy (become a minor Shinto god of storms earthquakes sea and natural disasters grandson of soosanol)
Grover (becomes a new pan god of nature and wild things and new inari god of wild things nature and foxes)
Luke (first adopted son God of family lions and bonds)

add on later

kiba (will become a shinto god of hounds and partnership, son of original pan and grandson of original inari)
sasuke (son of arieses, he will be the shinto god of madness and vengeance)
hidan (male hinata) (god of moon son of Selene)
shikamaru (will use shika) (Shinto god of shadows and night son of nyx)
shino (Shinto god of insects son of arechne goddess of spiders)
Areis
Nicholas (son of Hades shinto God of ghost) he goes with them finding the bolt
Gaara (shinto God of sand son of desert goddess)
Tyson (Percy brother)(God of water fire and steam)

orochimaru is good

disclaimer I do not own naruto or Percy Jackson. I will mainly use the movies and some book events I haven't read the books but I do now some things from it.