Before reading any further, you need to know that the transport and release of trapped animals, such as mice or squirrels, is regulated and may be illegal in your community.
Having said that, there are times when people want to live trap a mouse or squirrel, and this is one of the two times of year when people's interest in doing so seems to increase, based on google search terms that bring people to my site.
The short version for mice: Mice are granivores, so a wheat germ is to a mouse what bacon is to a human. Yumm. People often think peanut butter is great mouse bait, and it can be, but really, they are going for the grains. So, get some wheat germ and mush it up with some peanut butter for bait.
For squirrels, go here and heed that advice.
No matter what you do, there are people who will get mad at you so I would keep this to yourself.
I have only one more piece of advice to add to what is in the above noted links. It is worth knowing what species of "mouse" you are having a problem with. House mice are a commensal species in North America that pretty much only lives with humans. If you have a serious infestation of these, you may need a cat or something. Voles are very common "field mice" and are native to many parts of North America (sometimes they are called lemmings ... the names are not scientific terms so there is little sense in arguing over them), and would probably not mean a long term infestation but only the occasional invasion. Deer mice are wild field mice that are larger than voles, usually browner, and more differentiated in color from top to bottom often with a stripe along the side and a lighter belly. Depending on your house and where you live you may see very few of these most years, then the occasional boom cycle with a zillion of them everywhere. The best way to deal with the boom cycle is to wait a year!
You may have your own local folklore about these different species, and that folkore may be more or less useful. My point here, really, is just that it is not true that "mice are mice." There are multiple different kinds and they are biologically different.
I love the idea of an owl feeder! We've had an owl family in the neighborhood for the last two summers, I'd love to see them come back. I suspect they aren't around now, because squirrels have returned to our bird feeder.
Well, now your bird feeder is a raptor feeder!
I leave field mice alone - they're never a threat and at most are a nuisance when food is scarce. The house mouse on the other hand is as good as dead if I see it; in fact just the other night I swatted one, crushed it's skull, and tossed it into the garbage can.
Lots of mice appreciate sunflower seeds. Works well in a haveaheart trap. On he other hand for the snapping kind you need sticky peanut butter.
Sounds weird, but the most mice I caught was just having a bucket with some water in the bottom close by the porch. No bait. That caught more mice than the traps.
Friends of mine have a very mouse-plagued house. The resident 3 cats seem to be of no use whatsoever, though they do bring birds in through the cat door, alive and still ready to fly --- I've taken some outside and off they go. When my cat lived in that house, she was a dedicated and successful hunter, not so good at actually killing though --- as evidenced by the mice she gifted me in bed at night. Mice trapped in the Havaheart currently live a life of captive luxury until they are donated to a person who uses reptiles for educational programs. One mouse, so far uncaught, squeezes into the hamster cage to dine and uses the exercise wheel.
the most effective way i've found to trap the little mice in nyc apartments is by throwing a dish towel on them. i read it somewhere on the internet, and by god, it works. whether they're too weak or it just paralyzes them with fear, they can't get out - you just scoop them up and toss them in a bag and off to the park you go.
i damn well wouldn't try it with a nyc squirrel, though.
Well, they probably think "Oh, a dishtowel. This is novel!" and while they are contemplating that you make your next move.
I guess the NYC mice were the model for the ravenous bugblatter beast of Traal.