I have heard that there is a custom to eat oily foods on Chanukah.
What is the source for this?
Is there any source that the oily foods eaten on Hanukah need to be specifically oily from olive oil?
It doesn't seem like the contemporary commentators provide sources for the custom as Rav Mordechai Becher writes "Food fried in oil is also eaten to commemorate the miracle of the Menorah" and is echoed by Rav Y. Dov Krakowski at the OU saying,
There is a minhag to eat fried foods to commemorate the Miracle of the Oil. Such foods are likewise being used as a tool to commemorate the miracles of Chanukah thus integrating them into the Mitzvah of praising Hashem.
Although the custom to fry in oil doesn't appear to be particularly only olive oil, Rav Yehuda Prero has an insightful article describing the reason for commemorating the miracle with olive oil. Aside from the longer version you can see there, he quotes the
Aruch HaShulchan (O.C. 673:1) it is preferable to use olive oil when lighting the Menorah because it is easily drawn into the wick, its light burns clearly, and the miracle of Chanukah happened with olive oil.
Rabbi Dovid Orlofsky offered a novel answer as to why we eat foods fried in oil on Chanuka: We counter the Greek culture which focused on deifying the human body by eating fried foods that shows our lack of focus on beautifying the body.