Is the correct way of writing (and saying it) "Elven", "Elvish", "Elfin" or "Elfish"? Or something completely fifth? or sixth? Elvis? El Fin? Cocky Gringos?
I would personally say such things predate modern English (see Tolkien's comment re 'dwarvish' at the beginning of the Hobbit) and thus there is no 'correct' form. Use whatever u like.
They are the Olve in the ancient Oeridian; or Olven folk...which in the common tongue has become "Elves" or the "Elven folk". Tolkien would have called them the Eldar.