I wonder whether you could make an olive-oil-and-vodka (or something) cocktail, or if the oil would just separate. Only one way to find out... but the only hard liquor I have at home is rum, and I don't think that would be good.
I came up with a drink years ago called the Axis Powers: olive oil, sake, and jagermeister. There was a variant called the Barbarossa that included vodka. The best part was that I got someone else to make and drink it.