I use all my leftovers. I do not think olive oil, used cooking food is a problem. You just would not want to dump a large amount directly into our bin.

Go ahead and put it all in.

I do my vermicomposting in piles on the ground, and I've even dumped multiple ounces of oils into the compost with no discernable negative effect. In an enclosed bin, I probably wouldn't be so bold, but a little bit leftover clinging to food, and the little drizzle leftover from cooking won't make much of a problem, I'm sure.

Cooked food is no problem at all.

I agree with the above - small quantities of oils used in cooking should be fine, even with fried foods like french fries and such. But NOT leftover oils of any volume.

And yea, all cooked food leftover is fine - basically if it's vegetable and you would eat it, it's good for the bin (ok, maybe except for heavy onion and garlic).

"ok, maybe except for heavy onion and garlic"

well, I was actually a little concerned about this too. Almost every meal I cook includes both onion and garlic :P

Should I try to avoid raw/cooked garlic/onion or are small amounts okay? I would say I probably throw away about 1/4 small onion a day (between the chopped off ends and leftovers)

Don't worry about garlic/onion. Just don't dump in huge quantities of anything all at once.

I didn't mean to scare you off - I wasn't speaking of cooking with onion and garlic...what I meant for example was not adding (whole) onions and garlic as foodstocks.
Much like a liitle oil is okay, but dumping grease in there would be bad.