I had a couple of rats move into the engine compartment f one car that was parked outside - next to the MDX. The vehicle had been driven within 2 days before I saw them there so driving the vehicle doesn't guarantee they won't move in - but it helps.
I shooed them out of the engine compartment over to an adjacent wood pile - one almost bounced off of me when he scrambled out. I then put an electronic rat trap at the wood pile and got one of the rats within a couple days. I then checked the MDX and could see some droppings on top of the engine cover, cleaned it off, and then could see more droppings. I couldn't see any actual signs of a nest though including in the air filter area. I got a couple of wooden rat traps, tied them to a stick so if they went off I could retrieve them easily from the engine compartment, and set them it in there on top of the engine cover after the MDX was home for the evening. I saw that the traps went off a couple of times, but with no rats/mice in them, but it may have scared them enough because after then there were no more droppings in there. This is easy and cheap to try - just don't forget to take it out before driving the vehicle in the morning.
I wouldn't recommend putting mothballs in the the ventilation system - you definitely don't want to smell those.