Grew up around a fair amount of Italians in Pittsburgh…never heard of it.
Thanks for the helpful responses. Yes, as far as I know, the euphemism comes from it’s use in The Godfather but I thought it had spread enough to be generally understood. In order for it to work for my purposes it would have to be more widely known than the responses here seem to suggest. Thanks!
Zoff, thanks for the warning- I agree with you, bad jokes suck. But I promise this one would have been funny. It’s for a “roast” kind of event and olive oil is a reference specific to the person being roasted, so I can’t really use “construction business”.
Well, you could always make sure your reference to the olive oil business is connected to The Godfather. You could allude to the movie itself. People would probably get that without you having to be too obvious.
waves back I’m not actually Italian, but I sure know a lot of them. Uncles with pinky rings always gave the best birthday presents. 
Well, I’m in South Carolina, states away from the Mafia, so all my “knowledge” is from TV, movies, and books. That being said, no, I’ve never heard it called that. I’d know what you were talking about if you winked and said “The Family”, “the family business”, “waste management”, “construction”, or maybe “imports”. Or somebody might be “a big man in the union”. But not “the olive oil business”, no.
Well, according to my New Joisey friends, if somebody is “in the trash hauling busisness” and:
(1) doesn’t own a garbage truck
(2) lives in an upper-class suburb
…usually means that he is in the mob.