Okay, I read all 16 chapters before I would review. EXCELLENT!!!
Clever use of Odysseus--Harry is rather on a journey isn't he? It appears he's learning something about himself.
I LOVED how Sirius knew instantly who Odysseus Harris really was...and the denial, I think, has truly fallen on deaf ears. Sirius knows his Pup. I think it'll be Sirius Harry confesses to as a result.
Like George Bailey in It's a Wonderful Life, Harry's had a unique--if a bit twisted--opportunity to see what the world would be like without him. He's also been given the oppportunity to put it right in this parallel reality.
The interesting thing is that enough of the events and attitudes are the same, which allows Harry to address the issues resulting from those attitudes. Dumbledore's refusal to face reality concerning Snape, the collective staff's failure to see the foul behavior of the students as it goes on right under their noses, and the injustices heaped on innocent people.
In this reality, I don't think Harry likes his parents too much. They appear to be as useless as the rest. I have to wonder, though, if that's going to change as Harry's relationship with Sirius develops. And where's Remus? Peter's captured, so the "true" Marauders are reunited. I expect Remus will re-enter the picture soon.
There's so much going on here. So much emotion, so much intrigue. While Harry was down in the Chamber dealing with Ginny, I'm sure it was all he could do to keep from playing the boyfriend card. He still retains his feelings for her from his own reality and has to fight them. He has to fight them with Hermione, reminding himself that THIS Hermione is innocent of the sins of HIS Hermione.
This Ginny doesn't know him as anything other than Professor Harris and neither do any of his other "friends." Even though HIS Ginny dumped him for Neville, he still loved her. So much so that he threw himself off the Astronomy Tower. I think he could take the rejection from the twins, Hermione, and Ron, and whoever else, but not Ginny. That tore his heart out and there was nothing left to live for. THIS Ginny dredges all those feelings up, whether he wants that or not. There's no denying one's love from someone else.
Harry grew up isolated, so he's used to it, but it doesn't make it any easier. It helps that he's finally making some inroads with the Hogwarts staff, but it's not enough. He was still betrayed in his reality and those memories are still there and they still hurt. They drive everything he does in this "new" reality he finds himself in and he has to make the best of it without drawing too much suspicion. But Sirius knows...
Great job! I'm excited to see more!