Is it okay to use 14 gauge wire for my garage?

I've never heard of a 220 amp panel. That makes me wonder about your electrical abilities. There is no code restriction to keep you from using number 14 in the garage or anywhere else. Unless it is a local code. Your 80% figure only applies to continuous loads like heaters and motors. Not to general use outlets. You can use all 15 amps on each circuit. I see no problem at all with what you are trying to do with the 14 wire and 15 amp breakers.