Had this issue several years ago when the factory across the street closed the same time the city sewer lines broke. Get the poison and put it in places the dogs can not get to. (Behind the stove is a good one) Place the traps along the walls. (rats/mice NORMALLY run along the walls, only across open floor if the HAVE TO) You will need to find and fill EVERY single crack you can. I even had them tunnel up UNDER the cement floor in my basement and come out behind the basement steps though a cement dirt/rock covered wall. When filling cracks, stuff the cracks with steel wool FIRST). Good LUCK! Oh and by the way Cats DO WORK! I don't really like cats, but I have two of them, and in the Fall they earn their keep!
For small mice, I use fly sticky paper traps. Put them on areas where they usually run about. They will get stuck on the paper. Dispose them according to your will. This only apply to small mice. When the rats are huge, rat poison should do the trick. The problem with this is, they usually die in hidden places.