In my insurance claim handling days, rodent damage was a very regular claim. Air ducts are not necessarily where they favor. Have found them in door panels, above headliners, inside seat cushions, under rear seat, under front seats, in trunk storage compartments, engine air cleaners, exhaust systems, etc etc etc....
The best claims are when they start chewing/eating wires. Eventually with enough chewing the car dies, or warning lights come on, or accessories stop working. Then mechanics start systematically looking for the electrical failure. And then they deduce from electrical troubleshooting that the problem is inside the dash, or inside the headliner, and they need to disassemble further. And all that labor and time gets REALLY, REALLY expensive. I have totaled many a vehicle due to mice damage, as they can do between $5,000 and $10,000 worth of damage when they start eating up factory wire harnesses for safety systems like airbags, etc...or nest in a curtain airbag, or whatever. Harnesses are expensive to buy, and the labor to route the wires is insane due to the amount of disassembly required, and the salvage value of an unwrecked car is high. That combination = total loss. I'm buying your car from you on behalf of the insurance company and selling it as-is to cut our losses, go get yerself another one...we ain't fixing this one.
One of my favorite claims was when an owner's (large) dog spent the day under his owner's truck, grabbing/chewing/ripping every single wire, fuel line, brake line, heat shield, insulation blanket, and coolant hose he could reach, and destroyed EVERYTHING non-metal on the entire undercarriage of this truck. He went out and turned the key and got nothing. Couldn't figure out why. Towed to dealer. $12,000 of insurance money later, this $35,000 truck was back on the road. Not totaled because it was pretty new and truck had value. I don't know the fate of the offending dog.
I had another customer with a relatively new car where a mouse started packing food so far up the exhaust system, that when the owner tried to start the car, food nuggets got caught in the exhaust valves and the car lost all compression on a few cylinders. Ran like crap, warning lights everywhere, towed to dealer. Dealer diagnosed blown engine due to zero compression on 2 or 3 cylinders. Agreed to warranty engine. They then started disassembling to replace, and when exhaust manifolds came off a pile of dogfood fell out. There goes your warranty. Call your insurance company...now I get involved. I inspect the car, turns out there was no actual engine damage, the stuck valves didn't get rammed by a piston either, but the dealer still had to pull exhaust manifolds to clean the mess, and pull the heads off the engine to remove some valves and pluck out the dog food that was jammed into the exhaust valves. A couple thousand bucks in labor and gaskets, covered by insurance.
I have no advice on how to avoid critter damage. You can't beat nature, you just have to live with it. So park where you're gonna park, be alert to smells, leave NO FOOD of ANY TYPE in your garage or your car, EVER. Baited mouse traps in garages are wise at all times. And pay for comprehensive insurance from a reliable insurance company if you don't want to eat the whole repair bill when the weird thing happens...