I have much more experience in this area than I would like to admit. Here is what I've found:
If you actually find a mouse on a glue board before it dies, the process of removing it with vegetable oil will almost certainly kill it. I think they actually die of fright. Yes, we have tried this! I really think these are less humane than traditional traps.
The better mouse traps often catch the mice, but they don't hold them. We've had several get away.
I've never actually been able to catch a mouse in a live trap. I wish I knew how.
The electronic repellent things don't work worth a darn.
Poison scares me because we have pets and kids and also because we've had mice die in places where we couldn't get to them and that really smells BAD.
The good, old-fashioned snap traps are the only thing that has ever worked for me. They usually kill quite cleanly, not always, but more often than anything else I've tried. It's a dirty business killing the poor little things and I hate it, but I just can't live with them in my house. I also hunt down the cracks where they come in and stuff them with steel wool. I used to bait the traps just with peanut butter, but I actually had some mice eat the peanut butter clean off without setting off the trap. Now I use a pretty good-sized piece of bread with a bit of peanut butter on it. I've also found that certain traps are more trigger-happy than others which means a cleaner kill...when I find a good one I hang on to it. I really hate to admit it, but I've killed a huge number of mice in the last five years.
The other thing I've found is that you have to get them quick, when you first find the droppings, before they have time to reproduce or invite their friends in.
We would have a cat if we could, but my husband is very allergic to them. I don't know if that would actually help or not. In college I had a ferret that used to kill mice in my apartment. Just an interesting fact.
Keri, wife to Tony, mom to five DDs: M ('96), S('01), E('04), A('07) and J('10);