We do know where the chaos gods are situated pretty well in the warhammer world, but is there any piece of literature portraing where the pantheon of the empire "lives"?

something like the olympus for the ancient greeks for example? that discussion came up recently and i could actually not recall having read about that anywhere yet.

does some kind of "elysium" exist for people of the empire?

There has never been any "official" extraplanar address assigned to the gods of the Warhammer world. It's partly GW's infuriating chokehold on the IP, but there are also some ways that you can fictionally rationalise the ambiguity of deities in this setting (or at least ways that I've noodled it around so as to make things fun for story telling).

My 2 coppers:

Each cult has their own wholistic theology on morality, tradition and the post-mortem condition. That gives a lot of flexibility for every game group to sort of make it up as they go along. For example the Cult of Sigmar is good about relegating all deities that are not named Sigmar into a backup singer position at best, and outright burnable heressy at worst (depending on how bloody the Ulrican vs Sigmarite fued is that day). In terms of where he is? Well he's kicking the crap out of the beasts of chaos in the chaos wastes..no he's beating up Tilea because they're jerks…no wait he's actually IN the realm of Chaos choking out Nurgle. There is no unified "heaven" approach to the gods of Warhammer. Talk to ten priests of each cult and get about fifteen convincing answers on the matter.

Additionally there is a tradition of folk worship in the Empire where the holidays, myths and rituals of one community might vary significantly (spitefully in some cases) from a village 20miles away. Let's not even get into the crazy disparity between beliefs from province to province or from north to south, east to west accross the Empire. This has a lot to do with the permutation of the worship of the Old Gods, entities, and spirits of the ancient world before Sigmar arrived in his capsule from Krypton and held aloft his magic hammer and said "by the power of Ghal Maraz!!!" A lot of those old beliefs just got rebranded by conquering peoples and otherwise stayed the same. We have plenty of religious examples like that in our own world.

This is also why the concern over chaos worship finds witch hunters traipsing through the countryside. They need to make sure that a given town's spring time celebration to honour Taal isn't just some crazy orgy organised by Slaanesh. Or that bloody pitfighting conducted on the 18th of Sigmarzeit is really done to honour Sigmar and not Khorne.

I personally like having a total mishmash of what the "truth" is.

But if the vague nature of the deities of Warhammer is just killing your sense of fun. Just go with "They live in a good neighborhood of the Aethyr.." and move along to death and dismemberment and adventure!

..and the Jester ringled', they emerge from the Law gates at the East and West poles…

I like the idea dropped in some books of Warhammer where its suggested that the all gods (lawful, chaotic, evil…) are entities formed from the Aethyr by the emotions of living creatures. As where they exist, well in that case in the Aethyr what ever it is (by the way, you can read real discussions about the existance of an "ether" in not so old books of physics).

This also is consistent with the fact that the most venerated, worshipped or revered gods are the most powerful or with a greater impact in the warhammer world.

As stated, this is one of the things you can view as "GW frustrating vagueness" or "the fun blank spots the Warhammer universe leaves for you to sort out in your version, not even keeping same between campaigns if you want to mix it up and keep players on toes".

My take (consistent I believe with canon fluff but I welcome education) is that there aren't really places in the Aethyr - Warp, just entities. To the extent anyone talks of "being somewhere" in the Warp it's really "being with an entity" (usually being consumed by them actually). People in the Empire certainly believe they go to be with Morr and there is an itty bit of "fluff support" for that here and there (a ghost knowing someone was murdered after they died because "they wait for me with Morr" in a "I can see them in the light" kind of way) amidst the overall shroud that obscures the afterlife.

I like the "no places" idea as well because if any non-Chaos gods had a "place" the Chaos Gods would be assaulting it all the time etc. As an idea-fueled entity, Morr's realm is contingent on Morr continuing to be an idea humanity supports (thinking of it technically, as long as we create a safe-haven entity for our souls, it will be there - if Morr ceased to exist, the safe haven would and all souls past and present protected that way would be at risk of being a daemon-buffet). The dwarf ancestor gods are sort of the same deal for them would be my take.

nice catches.

we also decided to let them live in some vaguely defined "aethyr". in a dde campaign i once played we had a way to contact the gods in some sort of mystical hall in which each god had his own statue and you could talk to them in person. was kinda fun, but we never really found out where they were or how they existed. that little uncertainty of not knowing if you are really talking to the actual gods or if it was a trick and the whole thing made for a great game!

thanks for the ideas guys!