Aha! So Kayla and Kailina are the same; but there's more to be explained. After checking some more sources I think we can be sure of the existence of at least two separate Agaw dialects/languages (just like Bender 1976:8 says; but unlike Ethnologue and Sommer 1992): first, Qemant-Kemant-Chemant-Kamant-Kimantinya-Kimanteney, and secondly Kayla-Kaila-Kailinya (ethnonym Betə Israel (cf. Mann & Dalby 1987:16), xenonyms Falasha/Felasha from Ge'ez 'immigrant, stranger'; Yihudi (cf. Ethnologue 1992 as cited in Sommer 1992). Kemant could be extinct by now (Sommer 1992 mentions that "according to Gamst, Kemant is threatened by extinction"). In any case, a huge language shift is going on here; all speakers are bilingual in Amharic and according to Ethnologue, only 1650 native speakers of Kemant were left, out of an ethnic group of about 170,000 people in 1998. Endangered, to say the least.
Quirin (1998) leads me to believe that an important reason for Qemant and Kayla being separate languages is that their speakers (coming from a common Agaw base) developed separate identities from the beginning of the 14th century on. However, apparently there's a lot of fuss going on in Beta Israel historiography (cf. e.g. ) and I don't know enough about it at present to judge sources like this (though Qurin seems to have done his homework).
Anyway, a third dialect seems to be Qwera/Quara/Qwarina/'Kara of Kwarasa'/Hwara/Hwarasa; this one appears to be extinct (cf. Ethnologue). It seems to have been related more closely to Qemant — Gamst (p.c. to Sommer, Sommer 1992:358) proposes that "Quara, Quarinya, spoken by a few Falasha in Quara (to the west of Qemant-land), is nearly the same language as Qemant."
I've listed my sources below; we'll probably be able to use them in some of the articles. —  ✎ 00:28, 1 Apr 2005 (UTC)

Bender, M. Lionel (ed.) (1976) The non-Semitic languages of Ethiopia. East Lansing, Michigan: African Studies Center, Michigan State University.
Mann, Michael & Dalby, David (eds.) (1987) A thesaurus of African languages. Londen/München etc.: Hans Zell Publishers.
Quirin, James (1998) 'Caste and class in historical north-west Ethiopia: the Beta Israel (Falasha) and Kemant, 1300-1900', The Journal of African History, 39, 2, 195–220.
Sommer, Gabriele (1992) 'A survey on language death in Africa', in Brenzinger, Matthias (ed.) Language Death. Factual and Theoretical Explorations with Special Reference to East Africa, Berlin/New York: Mouton de Gruyter, 301–417.