That's kind of odd - 24 hrs. Normally a village sends out a letter stating the exact code violation & gives 30 days (or something like that) for you to comply / resolve the violation. Talking nicely with them also helps. Simply ask what you can do to keep your pets. It may mean getting rid of a rooster or keeping a smaller number, but it's better than getting rid of all of them.
If you have a child in 4H who is enrolled in poultry, you may be able to legally keep chickens. In DuPage County, we enroll in Sept but can change/ add things until March. By May 30th we must say what projects are being entered for the July fair. I think you're in Cook, but it's probably similar.
http://web.extension.illinois.edu/cook/4h.html
Before it was legal here, a few people I know kept 4-6 hens in their garage or a mini serama in a parrot cage in the living room. It's legal to own poultry in the city of Chicago, but there are a lot more restrictions for everyone in the suburbs. On the positive side, more people are going green, gardening, making rain barrels, etc, so your town could be open to changing some ordinances.