Is there a construction for a variable length block cipher that uses a fixed length one? I'm looking for some way to take a fixed length block cipher (for example AES) and turn it into a variable length one with comparable security. The new length may be bigger or smaller than the underlying block cipher's.

I'm considering going about this with an unbalanced feistel network, but I'm asking if there's an already accepted way to do this.
Yes, there is standard work on this. You should see "On the Construction of Variable-Input-Ciphers" by Bellare-Rogaway (PDF). They give definitions and constructions.