If there was a complaint submitted, they will provide you with paper or visit regarding the nature of the claim.
Until you know for sure what the nature of the claim is, don't stress out about it.
Simply don't put your animals within line of sight of the door or any windows that can be seen from public land.
If you have well built enclosures, and no hacked-together cages, if they do come through your place that's in your favor.
Should by-law enforcement press the issue, tell them you will fight the issue as far as you can and contact legal aid. Make a point of letting the city know that you will cost them a considerable amount of time and money if they continue to harass you.
Look for every case you can find of violent or threatening dogs not being dealt with by the city. St. Thomas has by-laws regarding aggressive dogs, but they refuse to enforce it unless the dog actually bites. If Oakville has the same policy I would use that as a counter to their biased position on "dangerous" pets.
DON'T move all your pets to another location, despite the advice given previously.
The moment those animals pass through your door they are considered to be in public, and fall under the "at large" bylaws. Ridiculous as it seems, transporting a snake/invertebrate/reptile in a vehicle on the road falls under that as well, and lets them prosecute you as easily as if you took it to the mall and let it go (at least under the interpretation of the law, it all depends on if the judge's mood that morning).
Don't give in without a fight, either way.