c. 1200, aluisc, "belonging to or pertaining to the elves; supernatural," from elf + -ish. Old English used ilfig in this sense.
Entries linking to elvish
elf n.
"one of a race of powerful supernatural beings in Germanic folklore," Old English elf (Mercian, Kentish), ælf (Northumbrian), ylfe (plural, West Saxon) "sprite, fairy, goblin, incubus," from Proto-Germanic *albiz (source also of Old Saxon alf, Old Norse alfr, German alp "evil spirit, goblin, incubus"), origin unknown; according to Watkins, possibly from PIE *albho- "white." Used figuratively for "mischievous person" from 1550s.
In addition to elf/ælf (masc.), Old English had parallel form *elfen (fem.), the plural of which was *elfenna, -elfen, from Proto-Germanic *albinjo-. Both words survived into Middle English and were active there, the former as elf (with the vowel of the plural), plural elves, the latter as elven, West Midlands dialect alven (plural elvene).
The Germanic elf originally was dwarfish and malicious (compare elf-lock "knot in hair," Old English ælfadl "nightmare," ælfsogoða "hiccup," thought to be caused by elves); in the Middle Ages they were confused to some degree with faeries; the more noble version begins with Spenser. Nonetheless a popular component in Anglo-Saxon names, many of which survive as modern given names and surnames, such as Ælfræd "Elf-counsel" (Alfred), Ælfwine "Elf-friend" (Alvin), Ælfric "Elf-ruler" (Eldridge), also women's names such as Ælfflæd "Elf-beauty." Elf Lock hair tangled, especially by Queen Mab, "which it was not fortunate to disentangle" [according to Robert Nares' glossary of Shakespeare] is from 1592.
-ish
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.
The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.