Ah, but if you watch the Six Ways Mushrooms Can Save the World/Earth, you can use a bed of Oyster mushrooms to "digest" oil. He was talking about petroleum oil but no doubt the Oysters will happily dine on vegetable oil as well.
Ah. But is that composting? That is the question isn't it? Remediating compounds in the soil, or dirt if you will, is one thing. Remediating compounds in an aerobic composting process is another. Mushrooms may grow in compost but do mushrooms compost?
So, you make your compost bin a happy environment for bacteria and their fun happy friends to digest things but then you have to wait until the oyster mushrooms kick in to finish off the nasty stuff. If everything is already unrecognizable from what you put in and all you're waiting for is the oyster mushrooms that may or may not kick in, are you composting?
All composting is bio-remediation of some sort but not all bio-remediation is composting.
I'm thinking vegetable oil will compost while things like petrol will take far more careful management, care and, control with mushrooms or maybe exotic bacteria that just don't simply arrive by a ubiquitous presence but must be seeded or cultivated in order to remediate the target substance.
Yes, you can compost vegetable oil but it will be harder than just mixing leaves and grass clippings, adding water and turning a few times. If the vegetable oil is a substantial fraction of the bulk of the pile it will take longer. A little bit of vegetable oil compared to the overall bulk of the bin will probably not have a noticeable effect. I would expect vegetable oil to be a rodent magnet so it should be buried deep with in the bin to avoid the odors.
Compost popcorn? (I forgot about that one) That's a gimmie.