Kodlak was rescued by the Companions, no? Or, rather, sent to Sovngarde. I can't judge whether he was serving Hircine at that time (while he was in Ysgramor's tomb) or whether he was fighting to go to Sovngarde with that wolf. So, theoretically, if you had "friends" that knew you were split between such mandatory "duties," they could fight off the familiar that represents the power of that God/Daedra (in Hircine's case it was a wolf). As such, I can make a hypothesis that a soul might just be stuck in an intermediate state forever. That, or the Gods/Daedra you serve won't really care about you, considering they're Gods/Daedra, and just send you to Oblivion or something. Which would create another interesting topic: Becoming a Daedra.
Most of this is just from memory, and I'm sure to have missed a bunch of lore books and other material written on the topic, but I digress.
*SPOILERS AHEAD!!!!!!*
Kodlak tries to resist, but admits that he can't for much longer. Considering that the events in Skyrim seem to indicate a rather fast progress at that point, it was likely only a few days.. Then you cured him. You can cure yourself the same way you did Kodlak, only before dying. Kodlak does seem to suggest that there will be a battle between the heroes of Sovngarde and Hicrine's hunting fields soon enough to claim the souls of the rest of the companion leaders should they wish it. So it's obviously possible for souls themselves to move between realms. I'd imagine, that this would mean that a powerful enough soul could freely travel between the realms and go where he or she wants, though that last part is speculation. I should note here, that Kodlak is likely speculating as well, as he doesn't seem sure and he hasn't really been to the "afterlife" yet so I wonder how sure he can be...
During Molag Bal his quest you need to get a follower of Boethiah to swear his allegiance to Molag Bal and break his oath with Boethiah, I'd imagine thus that you go to the realm of the Lord you swear service too, and that you can break these oaths. A Daedric prince would then however probably still be able to claim you, unless you get a new Prince that wishes to have you in their realm. The two could fight it out then.
Speaking specifically about the Dovahkin (assuming all quests are done), the only oath he ever truly swears is to Nocturnal.
Hicrine is just a coincidental side effect of becoming a wolf, at least I don't remember actually swearing allegiance to him. You were told of the effects before hand though
Shor certainly also has a claim because you are a Shezzarine...
And then comes every random Daedric quest in the game, each or near each one of them have dialogue options where you can swear loyalty to the prince. Never once can you remove that oath, so it's quite possible that you are alligned to all Daedra and Shor... As to whom of them would have the strongest claim I don't know...
Given the oath I'd imagine Nocturnal, given the actions you take I'd imagine Shor... Hicrine and all other Daedric princes seem like outcasts to me...