can anyone tell me what is oscar to edo? like does edo sees oscar as his muse or what

I think mostly Oscar reminds him of Hugo. You can see it in the guy he sleeps with in the story "Phantom", too. Edo asks him to turn around during sex, so that only the back of his head is visible. Edo is still hung up on his past encounter with Hugo, I think. It explains why he is so obsessed with Oscar and his relationship with Lily. He sees a bit (or a lot) of Hugo in Oscar and doesn't want him to experience the same fate. But that's just my interpretation.