While there are greater gods in the setting (in this case, the Chaotic mother-goddess Vesna/Marzanna and the Lawful clockwork-god Koschei), they are very distant and inhuman. They very rarely interact directly with mortals or with worldly affairs on the day-to-day scale. However, there is a huge number of minor Spirits present in the Mortal Realm and in the adjoining Spirit Realm, Spirits with which mortals can interact with directly, Spirits which have discernible influence over day-to-day affairs. These are the spirits of ancestors, the spirits of unique places, the spirits of old terrs or groves, of tall mountains and strange stones... Even the very minor spirits of a household (such as a Domovoi). Many creatures which are regarded, by D&D or S&W defaults, as ordinary "monsters", would be Spirits in this setting: dragons, elementals, dryads, fey, ablothes, beholders, even dire animals.
A Spirit is, first and foremost, an NPC. It can only be present in one place at any given time, and is not omniscient by any means. It can be talked with, negotiated with, fought and even defeated by heroes. Anyone can try and interact with a Spirit, even commoners, though Shamans and Elementalists have far greater chances of getting a good outcome from such interaction. Peasants leave bowls of sweet milk gruel on their homes' floor at night to invite their household Spirit - a Domovoi - to bring them good luck and help them keep their house neat and tidy; farmers leave offerings by the nearby forests' eldest tree so that the Dryad resident in it will bring them good harvests and keep savage beasts away from their children; nobles pay homage to their heroic ancestors to gain their blessing in coming battles; evil villagers might even sacrifice their first-born sons to a mighty dragon in return for good weather and bountiful harvests; and so on.
Many "Spirit" monsters - vampires, dragons, aboleths, beholders and so on - would die once and for all when slain, though slaying them in the first place won't be easy (to say the least). The Spirits of the dead which could be found on the Mortal Realm or close to it are ones who have a reason to linger there instead of going to the Realm of the Dead; "slaying" them would banish them to that Realm, but if they have a good reason to stay near the Mortal Realm (say, revenge, improper burial and so on), they'll return to haunt the Mortal Realm once again unless this reason is taken care of. When you kill a nature spirit, the result depends on its kind; slaying a wholesome nature spirit would cause the area to whither; slaying a corrupt nature spirit might be able to clean its taint from the area.
Spirits have both regular monster powers of their type and thematic Spirit powers - such as influence on weather or harvests in a given area or spells such as Raise Dead or Reincarnation. The more HD a "god" has, the more powerful its abilities. A Domovoi, for example, will have only minor cantrip-level powers helping to keep a household clean and free of vermin; a Dragon would be able to control the weather and find precious metals and so on.
During the Age of Blossom, the great Elemental Engineers created mighty contraptions based on advanced spirit-binding techniques. Essentially, they forcibly trapped elemental spirits/"Gods" in special clockwork receptacles, forcing the spirits to serve for eternity (until the binding is dispelled) as energy-sources for machines. The most common contraption was the Boiler of Endless Steam, where a fire spirit and a water spirit (a Salamander and an Undine) were bound to the same spot, endlessly producing a stream of hot steam and causing unimaginable suffering to both spirits; this allowed for very efficient steam engines without the need for fuel or added water. Of course, the spirits who broke free from such entrapment are typically VERY pissed off at mortals and might become extremely vengeful!
This is the cosmology I have in mind for my campaign world:
Essentially, the Spirit Realm is a combination of the Ethereal/Plane of Shadow/Astral/Faerie World and so on - a place very close to the Mortal Realm, overlapping in places, yet quite alien. The Realm of the Dead is where the spirits of the dead go - it is not a place of punishment but rather of rest; dead who have a strong reason tying them to the Mortal Realm (such as improper burial or great injustice) linger behind as ghosts, and can only be permanently driven to the Realm of the Dead where they belong if that reason is resolved. The Elemental Realms are the building-blocks of the universe.