When to use "Elven", "Elvish" and "Elfic"?
Okay, here goes: Etymonline's comments on elf reveal usage from the 1550s and stemming from the words elf, ælf, ylf. The plural mentioned there is "elves" which would match the traditional pluralization of lf: shelves; wolves. Unfortunately, there is no word for wolven so that doesn't help us much.
The same site does have an entries for elven:
elven - O.E. ælfen; see elf) [sic] + -en (2). Apparently obsolete until revived by Tolkien.
And elfin:
elfin - 1590s, from elf; first found in Spenser, who may have been thinking of elven but the word also is a proper name in the Arthurian romances (Elphin).
And elfish:
elfish - c.1200, alvisc; see elf + -ish.
Tolkien's usage of elven strongly implies that this is the appropriate term for his elves. The c.1200 usage of elfish seems appropriate for mythological or physical references to elves (his ears are elfish; their attitude is elfish).
(Edit per Martha's comment): That being said, Elvish is also the Tolkien proper term for their group of languages with the prime examples being Quenya and Sindarin.
As far as non-Tolkien usage, Wowpedia consistently uses elven in their article on Elves. Dungeons and Dragons appear to use elven for the language and adjective. Other fictional universes could easily vary. It would be best to check with their experts.
The summary: Elvish for physical attributes or mythological references; elven for Tolkien and most other fictional universes. Elfic is unused in English and not advisable.
The spelling with 'v' for dwarves and elves is from Tolkien.
I suspect (but am not remotely geeky enough to know) that he used the different spelling to give his imaginations a distinct identity compared to Santa's little helpers.
I think the two are commonly used interchangeably, but I think this is the difference.
If something is elfin it is "of, or relating to or made by an elf"
These shoes are elfin.
Something is elfish if it has characteristics of an elf.
Tom is short, and very mischievous. He is elfish.