In TES:O our souls are taken by the God of Schemes, Molag Bal. I understand that in the games creatures can be soul trapped but that soul can only be absorbed once the organism is killed, right?

So how does a soul fit into everything? What does it give to the organism, its consciousness, its ability to move (like fuel for a machine ala dwemer machines) or something else?

But also how will the PC in TES;O survive without their soul if this is the case?

simple, we were zombies to begin with. A highly fine quality zombie, so believable that we're alive.

Nah.

Actually, that's a damn good question. It involves with necromancy no doubt. I can hardly believe we're actually some kind of draugrs in TES:O.

Perhaps the PC has a second soul? Maybe given a temporary soul? or perhaps the link with the soul is not broken.

Hmm...no.

It has something with Princes realm, especially Molag. During TES:O, there was no Dragonborn emperor, and that meant Oblivion's realm had tighter hold on Nirn with nothing holding any connection established back.

Somehow, Jagar Tharn made a deal that makes our soul tie in that whatever realm that stored us in. That connection, it what made us... well some type of zombie.

Yes, souls, or at least some part of them, appear to contain the consciousness of a person in the TES universe. My take on what is happening in TES:O is that it is a result of the Planemeld that is taking place. If the Planemeld is indeed merging Coldharbor and Tamriel, then that makes Tamriel just an extension of Molag's realm where our souls are trapped. If it is just an extension of the realm, there's no problem with them being able to travel there as it is just the soul moving to another part of Bal's realm.