While one does not have to be aware of serving a god in order to be destined for that divinity's vault (hardly anyone who serves Mammon realizes it), the majority of souls do not have enough devotion to a specific god for their souls to be claimed by anyone. Any unclaimed soul is destined for Arawn's underworld. There they fashion their own heaven, hell, or purgatory, as they form the dream-scape of the fate that they subconsciously believe they deserve. However, the journey to the next world is not instant. Upon death a soul becomes a Sluagh, and experiences a strong urge to move on. (I'm not sure if they are all drawn to Arawn's vault and some are merely intercepted along the way or if devoted sluaghs are drawn directly to their gods' vaults.) While most sluaghs give in to this urge rather quickly, it is possible to have a strong enough will to resist this pull and remain on Erebus indefinitely.
I suspect that the resurrection of immortals works much the same way as the resurrection spell, except without the need for outside assistance from a spell caster. Resurrection only works before the Sluagh has left the plane of Erebus. No mortal is capable of calling a soul from another plane (except maybe with the Netherblade). (The Elohim employ special methods to capture the souls of their leaders immediately upon death in order to make resurrection easier.) For the resurrection spell to work on a sluagh that has already departed for its god's vault requires that that god first send it back. The only god who is known to have ever answered the prayers of a mortals and allow souls in his possession to return for resurrection is Camulos. Both Baron Duin Halfmorn and Charadon belonged to him and dwelt in his vault before being resurrected in the Age of Rebirth. Tebryn Arbandi and Arthendain also returned to life after passing to another vault, but their souls were allowed to return as a favor from one god to another (respectively, Camulos to Ceridwen and Arawn to Sucellus). (It may be worth nothing that although Arthendain is a hero of the Runes of Kilmorph, he was apparently not devoted enough to the earth mother for her to claim him. He passed on to Arawn, and came back because Sucellus wanted him to serve him by stopping Mary Morbus. It is unclear if Sucellus even has a vault now. He seems to be staying in Erebus in non-corporeal form, and the mortal souls he claims seem to return to live instead of being processed into angels.)