If person in Tamriel is related to some daedra or ascendented individual by its religion, its soul goes to plane related to that deity. There it serves as lesser daedra, companion etc etc.

When soul is soultrapped in soulgem its fate is related on what kind of soulgem is that. Normal soulgem, when is used for example for charging a weapon, simply transfers soul as fuel for that spell. Than, when that soul related charges are depleted, it continues to Aetherius. It also depends on what kind of magic is used for, because:

If soulgem is black, soul is doomed to soulcairn, somekind of purgatory. It can be pulled back to any plane by higher power, as we have seen in Sai Sahan or Lyris, as you sacrificed them to the Amulet of Kings and than meet them again at Dragonguard and Greymoor. Its BTW impossible because IDK if I learned that in Daggerfall or later in Morrowind, Soulcairn existence is simply mandatory to any magic possible in any plane same as Aetherius. So that gives me reason to think that soul tranferred there is conected to somekind of unibody soul like Gaia, fueling magic, for example, and can be separated only as new entity.

Curses and other pullbacks of souls, which wondering Tamriel, are related to similar mechanics but you have to think out soulgems as tools to it. Other tools can be necromancy, namely botched attempts, Curses, Magicaly enhanced individuals deaths etc etc.

Unfortunately nothing I wrote is related to any written in game text, because there are differences in books of Daggerfall from books of Oblivion, or dawnguard content. Its simply mess and noone really thought this right when these dogmatic mechanics was inplemented into elder scrolls universe.

I've not seen it explained in any ESO text, most of the stuff relating to souls and afterlife is found in the single-player games, and even there it's just bits or vague references you have to put together; or in unofficial texts by the original devs.

When mortals die, they go to the Dreamsleeve, where their souls experience the afterlife they believed in and are purged of memories for the soul to be recycled into the next life, in some other form (memories are water, this is ESO in-game knowledge after you do the quest for that one daedra outside the ayleid ruin).

The Dreamsleeve is also the area where dreamers go when they sleep, which means that all sleepers touch the afterlife when they dream. So basically dreaming is a reeanactment (or a pre-enacment) of dying. Dreaming causes a soul to act as if it had died. In a similar way, necromancy causes a soul which really has died to believe it is awake (which makes necromancy in TES games to be more like illusion or mysticism, rather than conjuration).

So yeah, sweet aside, Necromancy in TES is basically grabbing the soul in the Dreamsleeve and manipulating it into becoming awake/bringing it to Mundus, and then letting it fade back into the Dreamsleeve when you're done with it.

The Dreamsleeve can be explained by the wheel metaphor of TES cosmology. Picture reality as a wheel. Nirn is the hub of the wheel, the Aedric Earthbones are the spokes, and the gaps between the spokes are the realms of Oblivion. The Dreamsleeve is a thread going right through the hub; it goes through Mundus. We can think of it as a highway accessible through magic. Necromancy is basically trespassing on this highway.

To look at it in a more structured form, there's several states of being for a soul: alive / dead; awake / dreaming ; on Mundus / in the Dreamsleeve.

So a normal living mortal is: alive, awake, on Mundus.
A normal sleeping mortal is: alive, dreaming, in the Dreamsleeve.
A mortal who has died is: dead, dreaming, in the Dreamsleeve.
An undead mortal is: dead, awake, on Mundus.

There's lots of exceptions though, like Argonians for example, whose souls are recycled directly by the Hist (I think) so they don't really experience the Dreamsleeve.
Then there's the Dunmer ancestors who form the ghostfence (not sure this exists in ESO yet, probably not), whose souls volunteered to stay on Mundus to make a magical barrier and therefore also avoided the Dreamsleeve.

And yeah, people trapped in Soul Gems who go to the Ideal Masters, or in ESO's case to Molag Bal.

And then there's the even more interesting exception (not really explored in ESO) of Dagoth Ur. Because of the connection he made with the Heart of Lorkhan while he was guarding it, when the Tribunal killed him he didn't really die (as the heart was "the heart of the world"). That made Dagoth Ur: dead, dreaming, on Mundus. And when he sleeps on Mundus, he becomes dead, awake, in the Dreamsleeve. These states should be (and are) impossible.

To talk about Daedra though, they're not really alive to begin with, although they do have souls (or we can think of them as being souls, or being like souls). But it's been constantly referenced in the games (pretty sure that in ESO as well) that they just manifest on Mundus, while still being a part of Oblivion in general.

Oblivion is hell, and Aetherius is heaven.That's how I see it.

Mortals who've made pacts with Daedric Princes go to the respective realms in Oblivion (the Deadlands, Coldharbour, the Coloured Rooms etc.)
Those who worship the Aedra go to the realms of Aetherius (the Far Shores, Sovengard, the Sand beyond the Stars etc). We know for certain that these are distinct realms like the Daedric planes because we visit Sovengard in Skyrim.

The ghosts stick around because they have unfinished business on Nirn. I've seen this in quests where the player helps the ghost who then feel at peace and leave for whichever plane of Aetherius they belong to. They pretty much do this at will. But some ghosts are trapped by trauma/ necromancy/ curses/ etc.

There are also pockets of timespace between Nirn and Oblivion which are like alternate realities (I've only ever come across this in the Summerset DLC quest).