While I was looking for a source for oily food, I did find that almost all the major Poskim mention the custom to eat cheese or a cooked cheese dish on Chanukah. I also found that the major books on minhagim also bring the minhag of eating cheese; however, none of them mention oily foods. There is an article in the Hamaor saying that latkes are a recent happening. Another strange thing I found was a Pesach ad that was run in every edition of the Hapardas journal and included in it was latkes for Pesach, but there were no ads for Chanukah latkes. So my search for the oil continues. My sources are:
The Ran in Shabbos- c1_RanShabbos21b
The Bais Yosef OhrChaim675 – c2_BeisYosefOrhHaChaim675
KalBo- c3_KolBo44
Levush – c4_Levush670
Eliyahu Rabba – c5_EliyahuRabahOrhChaim670
Rama ShulchanAruch – c6_ShulchanAruchOrhChiam670
Chayei Adom – c7_ChyeiAdom153
Mishneh Berurah – c8_MishnehBerurah670
Kitzur Shulchan Aruch – c9_KitzurShulchanAruck139
Aruch HaShulchan – c10_AruchHaShulchanOrhChaim670
Ben Ish Chai – c11_BenIshChai
Kaf HaChaim – c12_KafHaChaimOrhChaim670
Yakut Yosef – c13_YalkotYosef
The Minhagim Seforim:
Lekutei Minhagim –c14_lekutiMinhagim
Taamei Uminhagim – c15_TaameiHaminhagim
Otzer Dinim Uminhagim – c16_OtzerDinimUminhagim
The Hamoar article – c17_HaMaor Jan-Feb93
The Matzah ad –c18_Hapardas ad