How do you deal with mice problems?

How do you deal with mice problems?
I knew I had a problem with mice getting into my garage in winter but I’ve never known how bad until I got adopted by a cat about a month ago. She has fetched about ten to my door and I’ve been in the garage this evening and noticed a plastic bag has been chewed up so I set a couple of traps with strawberry jam and have just got my first mouse.
My garage is really cluttered at the minute and there is nowhere else for the clutter to go.
What do you use on your traps?
How can I go about being more effective?