This is one of those areas that may have differing interpretations based upon the particular typica used by the jurisdiction or parish. Most Slavic parishes I have run into interprete oil as any oil whereas the Byzantine (Greek Orthodox, Antiochian, and Alexandrians) interprete it more strictly to mean olive oil alone. Every bishop publishes his Typica for his diocese based upon the Traditions and traditions of his culture and jurisdictional practices. For example Blubber, a mammal fat, (whale fat) is allowed in Alaska because it provides the necessary high calaries to burn to keep the native Alaskans healthy in their extremely cold climate, even though it is Great Lent or the Nativity Fast.
In general all jurisdictions fast from Olive Oil of Wednesdays and Fridays except those feast days classified as Polyelos days in which both wine and Oil are allowed to be used on a fasting day. Saturdays and Sundays in a fasting period are Wine and Oil days. Some jurisdictions may expand the no oil use to all oils including light vegetable oils like soy, canola, and peanut oils.
When in doubt ask your priest. My priest who personally fasts from all oils on fast days will respond that our jurisdiction fasts from Olive Oil only as that is the typica in use in the diocese. He does this even though he personally as a spiritual practice eschews the use of any oils on fast days.