A couple of years ago, we had a few mice decide to come and stay in our garden shed, due to my stupidity in deciding that the shed would be a great place to store sacks of bird food! Of course a mouse discovered my stash and decided to move in and raise it's family there. The shed is attached to the back of our house/garage and the mouse and family members had a great time climbing and exploring in the garage roof, we heard them scrambling around which is how we discovered their existence. As I am a real softy and animal lover, I would not let my partner kill the mice. We discovered that the mice had made a nest in the shed, it contained a few youngsters (they looked really cute, fat and furry!) that we managed to catch quite quickly. We then set traps and did our best to get hold of the rest of them. Once we got hold of them all, we counted over 14 at that stage and we took them out into the local forest and set them free. We returned home and removed all the bird seed from the shed, but a few days later, heard more scrambling and scratching and found that some remaining escapees had simply built another nest in the same place! We caught another seven mice this time and released these in the same place as the last lot. Thankfully we either had actually got the lot of them or the last remaining few disappeared once we had removed their food source. We too were surprised at how quickly they had grown from (presumably) the one mice into over 20 in a few short weeks.
Hope this gives you some idea, best of luck in getting it sorted out, personally I would prefer to see people using a humane way of catching them as per my experience, but appreciate that this may not be possible if they prove to become a real problem in your house. best of luck! Sue