Glass works fine in the microwave. It can get hot though, so be careful.
You do need to remove the lid as metal doesn't do well in the microwave (you might want to put a paper towel over the opening so you don't get oatmeal splatter inside of your microwave).
I haven't actually done this, but I'm a school trained cook (so I've had food safety classes) and I have a lot of experience with canning.
You should put the oatmeal while it's still very hot in very clean (or even better - sterilized jars) and then cap them. As it cools the jars should develop a vacuum and the lids should seal (even if you're using old seals - more on this later). This will keep out any bacteria or mold and the heat of the oatmeal will have killed any existing bacteria or mold spores in the oatmeal and also in the jar.
Oatmeal by it's self isn't actually a very good host for bacteria, and would quite likely be safe even if you didn't can it like I said above. But why take chances?
Lids: if you use new seals you can't use them again for canning purposes. However if you keep them specifically for the oatmeal you should be able to reuse them.