To begin I must say that I am a mythology freak and see mythology in everything.
Zeus (flying), Ares (fighting), Hephaestus ((fire), rock and steel)
I made a link between Ares and fighting types for the following reasons:
-He is the god of war
-He is aggressive
-He is precise and compact
-He wasn't really mentally powerful
Ares has a lot of similarities to fighting types first of all him being the god of war. He was a very aggressive bloodlusting god that saw killing or hurting as the only option (fighting types). Easily being outsmarted by agiler, older more experienced gods Ares might have been the god of war but could mentally and physically easily be destroyed
Zeus as the flying type seems clear to me. First of all he is the god of the sky. A cunning, decisive, agile, sly, wise, powerful god (trait of flying types). Comparable to birds Zeus knew when to strike at the right moment. His attacks were not always powerful but because he could easily hit weak points (abilities that come to mind: Big Pecks, Keen eye, Super luck,...) they where always critical. Often turning into an eagle when he needed to outsmart an aggressive or warlusting situation.
Hephaestus is my counter to Zeus. Not that he was more powerful then Zeus but was one of Zeus's favourites, even though he wasn't his son. His blacksmith. Hephaestus often got away when he was in trouble and never got punished that hard (rock, steel resisting flying type attacks). But then again Ares was Hephaestus's biggest enemy due to the fact of him sleeping with Hephaestus's wife, Aphrodite. For this reason Ares was also more of a counterfeiter to Hephaestus and easily countering him (rock and steel are weak against fighting types)
This seems logic to me but this is just my theory
Zeus beats Ares but isn't very effective against Hephaestus
Ares beats Hephaestus due to him steeling his beloved Aphrodite
Hope this made some sense