Some great feedback. Here are a few additional points I think should also be considered-
I do think Oma is quite powerful and do have some of the same concerns. I agree that Oma should be affected by some if not all CC effects. I do also think that he should be easier to kill when his host is killed. Personally I think a better way to handle this would just be to reduce his base HP. As a hero that ideally never engages an opponent directly, it makes little sense to me that he has a large base HP pool. It would fit with the character more in my opinion to have him be relatively fragile when expelled from his host. You could adjust the percentage of his HP that is given to his host to balance that aspect to still give an appropriate HP buff when As One, but given Omaeus ethereal/behind the scenes nature, it seems odd for him to be so durable.
One thing that I will say is that I don't think he needs as serious a balancing as Pham states because you have to consider that to utilize him, you're giving up having a third autonomous hero. This means you can't cover as much ground, can't surround enemy heroes as easily, etc. And Oma is fairly useless without his host, so in a 2v2 (2 enemy heroes against Oma + host), if the host is killed, the other team wins that encounter, regardless of if they kill Oma or not. Oma is going to turn tail and run in that scenario and has little ability to continue fighting without his host.
Your concern about his synergy with Frost rune is valid. Would it be possible to have frost not apply to Omaeus attacks when he's As One?
Completely agree with what was said above and want to add something. An additional problem with Ruriks ghost is that if you're attacking a tower and Rurik defends, you can forget taking the tower even if Rurik dies. This is because if you stay and eat Ruriks ghost damage to try to kill the tower, his burn very quickly kills the minions who would tank the tower for you. So you either turn tail and run, leaving the minions who can tank but not kill the tower themselves, or you stay and try to damage the tower yourself, in which case the minions die leaving you able to damage but not tank the tower (especially in addition to the overly strong burn aura). I'm sure you can see the game balance issue when a hero can completely deny destroying a tower just by dying near it.
PvP Game Duration-
I think the easy fix for this would be to speed up the rate at which your power increases in global PvP. Certainly not to the rate that it is in Arena, but currently the power increase is such that even with good play it can be difficult to be anywhere near 100% power after 10 minutes. Either a flat increase in the rate that power increases, or a scaling increase based on the length of the match would help.