A mouse can get through a half inch gap. What I would do: temporarily put the cage in s new place, because the mice - there are more than one by the amount of poo - have it on their radar. If you can elevate it with a block underneath so they can't climb past the overhanging edge, that's good too. Next, DON'T use poison like D-con. Poisoned mice live long enough to be eaten by raptors like owls or hawks, or by foxes or cats, and the poison will kill them. I hate it, but you must trap them. You can use regular mouse traps, setting them at night, especially near areas where you can see poop. Or you can use live traps and take them far away, but understand that they will probably not survive where you release them. Most important is to mouse-proof your home and the only way to do that is to close off every tiny gap where they can come in. This time of year mice are looking for warm places to nest. You may have nests of mice in a wall, attic, or basement space, under a counter....it can take a while to figure out where they are getting in, block every tiny hole or gap, then find and remove the mice already living inside. I'd do it - they can transmit serious diseases to you and your fids. Just be patient about finding all the entry points as it may take a while depending on your situation, but don't delay on getting and using some kind of trap.
Yes!! Be thankful the problem is with mice, not rats. I had a terrible rodent problem in my last house, and the exterminator service offered "mice are dumb, rats are smart." Once they are removed and the detritus cleaned, the best offense is definitely to rodent-proof your house. Literally every gap must be sealed - this takes time and attention to detail but absolutely critical. Please don't delay; once entrenched their reproduction powers are legendary!
Truly great advice! Your location in this huge Country can bring you additional problems, if you have a shared wall between you and your neighbor!
Adding just a bit the the above Posts: Start outside with a insulting foam product. I recommend a product by DOW call: GREAT STUFF, Insulting foam sealant PESTBLOCK. It is a high-density, low-expansion insulting foam product. Have plenty of paper toweling and a 1" plaster knife to flatten /smooth the form. Apply in small shots, there is no reason to over load. If you need more, add a little is better than over-killing with the first hit.
Once you start with this product you really want to keep going. So, with a roll of a bright color painters tape, first slowly tour the exterior of your home noting and marking any areas from very small to OMG big holes, cracks, etc... Pay very close attention to utility connection /piping, electrical outlets, exterior water shut-off /connections and also any place those wonder people from our Telephone or Cable accesses - both old and new. Now repeat from the basement using a flash light (the new LED lights are really good). Double check where the electrical and piping comes in though the wall (foundation). Also all along the foundation (sill) and the side walls. Check behind any electrical panel or meters if you cannot find thru wall pipe. Also check the cloth dryer vent pipe.
While you're outside, remove any brushes and/or earth that is against your foundation and side walls, especially any wood surfaces. Also, a great time to have a spray can of bug guard spray.
If you have not done this before, expect to be very surprised at what you will find! Some problems may require replacing wood boards, patching your foundation, etc...
Also, remember to look around the doorways and foundation windows.
Eliminate excess and food sources, and you will quickly get on top of this problem.
This will also reduce your heating costs a little bit this Winter.
NOTE: If you rent, check your contact before completing any work. If you own a home with a shared wall, check your buy /sell agreement regarding rodent /insect problems.
There is no kind way of dealing with mice. The old fashion mouse trap is still be best and safest way of killing them. FYI: As stated as part of another Post: Rats are Smart, they watch when mice enter and soon follow.