I fry onions and make them almost crispy like onion chips. So they are one step above caramalization. Then I drain them on paper towels to get them dry. I change several paper towels to get them completely dry. As they cool they get more crispier. You can use these onions in stews, as topping for potatoes, soups and countless other dishes.
I store mine in an airtight container and they last for months. Although I always use them up by then or I am sure they would last even longer. I also live in Chicago and our weather is generally cooler. You can even put it in a ziploc and store it in your refrigerator for months.
I can give you one tip if you did not already know. To make these caramalized or crispy onion process go faster do the following.
Slice the onions thinly and spread them in a large tray. Let them sit overnight in an open place (keep a window open or put it on a deck if you have one (I cover mine slightly with a cloth towel). The liquid evaporates and the onions get drier and shrink in size. It's much faster to fry them because they have less liquid.