The best and most permanent way to stop mice in your home is "exclusion" or "building them out" -- eliminating any openings through which they can enter. It's especially important you mouse-proof any areas where you store, process or use food. Make sure that, in addition to looking for holes in your walls, you also check electrical and plumbing entrances, doors, gutters, vents and chimneys for rodent access. Seal any opening that is larger than one-quarter inch (0.6 centimeters). Although mice can't get through them, it might be a good idea to seal holes that are smaller than this, as well. Mice are known for chewing their way through things, so before long that small hole might just be big enough for a mouse to get through.
Don't use plastic sheeting, wood, rubber or a screen to close off an area because the mice can gnaw right through it. A mixture of steel wool and caulking compound makes a good plug to seal small openings. You can't use steel wool on its own because the mice will be able to pull it out or chew through it. The caulking compound makes the patch surface smooth so the mice can't get through it.
You may want to try copper wool instead of steel wool for several reasons. Because of the way it's woven, copper wool is said to get stuck in rodents' teeth, making it difficult to move or chew through. This means you'll be able to skip the step of mixing the material with caulking compound before stuffing it into the holes. Also, while steel wool is known to rust, copper wool does not, which means you don't have to worry about rust stains on your brick, wood siding or internal walls.