Worms will eat your garbage -
They will eat your manures (stay away from domesticated animal manures like dog and cat), they will eat shredded paper (none of the slick stuff), they will eat your leaves and grass, they will eat your cardboard, they will eat your saw dust (wood shavings), and they will eat your food waste. In particular they love - coffee grounds, cardboard, melon rinds, and all sorts of "sh_t."
Manures mixed with wood shavings is a great combination. Melon rinds are great if you have a mite infestation.
Shredded paper and leaves are a great layer to add after you layer on food waste. I really mix these things up in the winter to get some good composting action going for the colder temps. In the heat of summer you need to keep things simple to produce as little heat as possible.
Use some kind of processor for your food waste to get the pieces small. I use a butcher knife or a food processor on pulse. My neighbor saves me all his waste from his kitchen in a bucket. I don't process any of that, I just dump it into my worm bin. But when I go to the grocer and get food waste from the produce department then I process that because it is all still whole. The processing is just so the composting process will move along faster.
It's not so much that worms are vegetarians, because really they aren't. They will eat anything that has lived and died.
However, there are a lot of other critters that are attracted to meat, and fat, and bones. And, since the decomposition rate of these are much slower, they are not a desirable addition to your worm bin, or any compost bin.
Therefore, you do not want to add, meat or bones to your compost system.
Dairy products? I wouldn't dump a load of cheese or dump old salad dressing into the system. But if you have a dinner plate that has uneaten salad with dressing and some grated cheese on it, go ahead and dump it in the compost bucket. Your system will handle it just fine. Bury it and cover it with a good layer of bedding and let the composting begin. There isn't much of anything that your system can not handle in moderation.
Citrus peels are something I am very careful about. While I don't worry about the peel from an orange or two, if someone had decided to juice a bag of oranges for orange juice I would not put all of those peels in my worm bin. There is a substance in citrus peels that the worms don't seem like too much.
Likewise, with oak leaves or pine needles. While I would not worry about a small amount of these in my worm bin, I would not dump a load of either of these items in my bin as well. The outer coating on oak leaves and pine needles is very slow to decompose. And yet in nature these things do decompose quite nicely in time. The tanin is a substance the worms don't seem to like either.
Another thing I watch for is making sure that any manure I use has composted at least 6 months. There are some exceptions. Rabbit manure, because it is not a "hot" manure, can be used immediately. As a matter of fact rabbits and worms are a great combination. But that's for another post.
Here in my neck of the woods we are soon going to be rolling into the time of year when the worms are going to be getting active again and the feeding will begin in earnest.