Wow, you really hit a bad podhole! Those look like steel rims. Given that they're steel, you can bend them and not have it be a problem structurally. So, I'd remove the tires, and use a pliers to try to bend the rim back into line where it's flared out as shown in your picture. But you should just buy an old 27-inch wheelset with aluminum rims on eBay. You'll shell out $35 or so, and the wheels will be lighter.
How do I know they're 27-inch? Just an educated guess, because I don't know of a steel rim ever made in the 700c size.