About the bovine origins: The juges of Hades stated that every king is to have a special child blessed by blood and ichor of an Olympian taking the shape of a bull and this is a long-standing tradition from the very creation of Crete. In king Minos's case he only had one special child and that is Asterion. I assume that the children of the special child would also inherite some of the bovine blood, but im not sure if Asterion's family members survived the war, the only one i know of surviving is Ariadne (that traitor b***ch) since on Lord Dionysus's vote in favor of Asterion he said that he saved her from the island after Theseus betrayed her (serves her right). So it's not impossible that she would have a child after living as a refuge or smth , but the main reason why the bovine blood was preserved is because of the tradition, the bull descending every generation so i don't think that her descendant can be Oscar's father.
As for the differences between Asterion's and Oscar's bodies (junk, nose ...) i think that it might be because in Asterion's case the Olymian was in the form of the bull and the mother was of creitan lineage but in Oscar's case Poseidon was in human form and the mother was a normal women who was never blessed by Gods. I am not 100% sure this is the reason it could be just the artist playing with different designs.