Ugh.
We get mice in our sheds...peppermint oil sometimes seems to work to keep them from settling in, but not always. They really like building nests in the center of the snowblower.
We've had rats outside before...a neighbor's shed had them nesting underneath. When the shed was taken out (thank goodness their Beagle forced the issue by tearing open the bottom of the building), the rats disappeared. At least I haven't seen any since.