How fun! I had a mouse nest in a gas BBQ once, it made a really cozy place to live I guess. There's not much you can do but deter, poison, or trap them - if there's a 1/2 inch opening they can get inside.
I've also had them inside our outside HVAC units. One managed to arc itself across a 240V relay. That was a mess.
For what it's worth, one word of caution with the sticky traps - they attract birds, so it might be a good idea to put them where other creatures can't get to them. I found this out twice the hard way and both times were bad experiences for the bird and for us.