Note: According to the Dwarf Fortress wiki, the content of this suggestion contains minor spoilers.
Currently, the various "flavors" of strange mood, with the exception of the fell mood, are somewhat frivolous and don't really add that much to the game. All they really do right now is slightly encrypt the material requests. They certainly need to be more interesting, and while I can't think of any way to make the secretive and macabre moods more interesting (and if nobody else can, then maybe they should just be removed), I have a thought for the possessed moods.
Possession would be actual possession: a dwarf (any dwarf!) could be possessed by the spirit of a dwarf that never had a strange mood before they died (though if they died from failing to create an artifact, they can't possess anyone). If the strange mood is completed, then the dwarf that was possessed still wouldn't get the experience, but the artifact would count as being the artifact of the spirit that possessed the dwarf, so the dwarf could still make their own artifact. If the strange mood does not get completed, then the dwarf that got possessed would be cursed—I'm not sure whether this would just be a curse of insanity, or whether it would be something else. (This is something that I'm a little dubious on—I tried to think of a way that the possessing spirit could get harmed, but I couldn't think of one.)