Due to lack of many resources on this, alot of the material is derived from The Kitsune Page. After spirit Kitsune, the essay had ended as far as elements go, so most will be my own speculation. As always this is subject to change as more research, hopefully my own digging later, is done.
Some cultures belive that a kitsunes powers are derived from one of the 13 elements. The elements they inhabit supposedly get a strain by the kitsune's presence due to what is require to sustain it. This can sometimes harm the land until its departure. Also their elemental state allows them control over those elements.
Celestial (Heaven/Tenko):
These Kitsune are commonly called myobuThese kitsune have abilities ornate to the heavens and draw their energy from things such as stars or even the heavens themselves. This allows them to pose no real threat to their surroundings because the stars and heavens are not only great energy sorces but not earthbound themselves.
Dark (Void/Reiko):
These Kitsune probably would be thought to be the opposites of Celestial. While not exactly true they do have their own set of unique abilities. They are said to have the power over things like life leeching, summoning dark creatures, or simply being able to hide into darkness with extreme efficiency. Note, this does not make that Kitsune evil in a sense. They supposedly make up a fourth of all Kitsune.
Wind (Air/Kuko):
These Kitsune are at home with the skies, having control of winds, gusts, and the like. They can create fogs and mists to shadow themselves or searing winds to deter foes. They draw their energies from the movements of wind and air currents, sometimes leaving the atmosphere stale and unbreathable as well as calm in areas most desired like the oceans for sailors.
Spirit (Kiko/Koryo):
Considered ghost or demon foxes. This element confused me the most as Kitsune are inately spirits, but of course to remain consistent with the 13 elements, it makes sense. As to what they have ability wise I can only assume easier control over the spirits of others and possession. As for the energies they draw off of, I can only assume spirits, being the most typical vampire of them all.
Fire:
Fire, some belive to be the most important to all life. These kitsune can harness it the most, using it in everyday things as lighting and warmth to destructive or productive proportions. As for drawing from the energies I can assume that they leave fire dead almost like blowing out a candle, or things like magma cold and lifeless as well. They might be able to draw away warmth from other things too, such as body heat.
Earth:
Now here seems to be a fun one. These kitsune are in tune with the natural terrain, maybe moreso the land itself rather than the vegetation. They can probably generate movement within the land such as earthquakes, landslides, or even raises such as hillsides and mountains. Their drawing of the energies can lead to the soil becomming barren, dry, and most likely unfertile for life to grow properly.
River:
One of a few similar elements I'll have to look into. These Kitsune control the streams and the ebb and flow of water in them. They can cause swells and droughts in the normal. Some myths and legends lead one to belive that sources of water also have healing and nourishing powers and Kitsune could easily be the same way. Their feeding effect can probably generate a drought or leave the water unclean and unlivable, killing the life in it and hurting those who drink from it.
Ocean:
The other half of a confusing puzzle for me as stated prior. These Kitsune control the oceans and most likely follow the same lines as river Kitsune. Some more related powers might be whirlpools or other destructive ocean oriented disasters. Their drawing effect probably leaves the same results as the river Kitsune.
Mountain:
Much like their earthen breatheren, these Kitsune control the terrain of mountains. While maintaining roughly the same hold on the land, I'd assume these Kitsune to be able to make minerals and elements more refined as it deals more with that than soil which could be organic. Not too much difference in their energy drawing except the effect, probably leading to rock slides, stress cracks, and other disasterous climbing terrain.
