1752 - Orion is born on Apokolips, the son of Darkseid. he is traded to New Genesis to seal their non-aggression pact.
6 years ago - Orion first meets the Justice League when Big Barda & Scott Free come to New Genesis to be married by All-Father.
2 years ago - Orion joins the Watchtower at the request of the All-Father to help fortify against Maggeddon.
1 years ago - Orion helps defeat Maggeddon & returns to New Genesis.
There's very little not to like about a god-like character that all the other god-like characters are terrified of.
One of the main reasons you have to be really careful how much you let the world of the New Gods interact with the DC universe proper is because the levels of power of these different characters need to be equalized. It's understood that some characters might be able to go toe to toe with Superman, but even those guys are unable to do what Superman can do when he has enough narrative weight behind him. There are only a few characters that can do that; be as strong as the story requires them to be. Orion is one of them, and therefore his appearances need to be carefully regulated.
We've established the main narrative thrust of the New God's involvement with Earth to be Mister Miracle's, using his story as their central arc. This allows Big Barda to retire to Earth, but for the rest of the New Gods to function mostly in the background. By doing this, they can be shown as being immensely powerful near-immortals without them unbalancing the narrative of the rest of the Heroes of Earth. We're still able to include his membership in the Watchtower, allowing him to be the overpoweringly ferocious force of nature that he is.