The best thing to do is get this product or something similar from Home Depot or Lowes
It's called Contrac Rodent Pellet Place Packs
They will eat through the bag and eat the content and happily go peacefully to a never awakened sleep.
This is a blood thinner. the same stuff you doctor gives you. It's mixed with wax and oatmeal. Trust me on this it will work. You may want to place the bag on sheet of cardboard so not to have a mess on the floor.
This is as humane as you can get. Also make sure there are no holes in the room(s) where mice can get in. Mice do chew through most anything so check for holes outside your home to and seal them. It can get pretty bad quickly if you don't take care of it right away

Ya, that's the warfarin stuff. It does work but as noted they tend to go and die in the walls which causes a stink.
 
Also what I didn't mention is that their decaying corpses within the walls can muck up any insulation, wood, drywall, etc. It's minimal damage if it's only a few mice and not a HUGE deal but it can compromise the nice tight seal a meticulous insulation install provides. Lots of mice? That can get real yucky.
 
I've done lots of demo where you pull back the walls and you see all these carcasses and how they mucked up the innards of the walls. Again not a big deal but still.
 
And a reminder that if you have cats/dogs/whatever and they catch one of the poisoned mice and eat them it can seriously screw up their guts (vet bills, nasty poops, general unwellness or worse for smaller pets).
 
Seriously the steel wool, blocking up entry ways, removing all potential food sources an the like will get rid of those buggers for good. Without those types of steps being taken on top of any other traps/poison/etc methods your're just gonna have to keep massacring the little buggers.

Now raccoon infestations... OMG! That is some twisted and potentially dangerous action. Especially fearless, well fed city raccoons.
 
I've had to go toe to toe with those bastiges far more than I'd like to mention.
 
Even woke up with one a couple feet from my bed staring at me. Thought it was my roomate's dog at first. Nope. Big, fat, nasty raccoon watching me sleep. Grabbed my bat and started smashing stuff trying to scare it back out the window. It did NOT give a flying fart. It eventually, in its own time, bumbled its way out so fortunately I didn't have to kill it but that was not a cool way to wake up.
 
I put a baby gate over the window after that. In another incident (that did turn gory and I won't elucidate) my roomate got bit and scratched and had to get all the belly jabs in case of rabies.
 
Not cool.

My recommendation?
 
Well, as one legendary rodent control expert says:
 
“In order to conquer an animal, I have to think like an animal, and whenever possible, look like one.” — Carl Spackler 
 
He also recommends using plastic explosives for particularly stubborn rodent infestations:
 

 
HTH

There are humane mouse traps. Google Havahart.
 
Sound advice from a vegan cat.

 

Cordless mouse.

Slugbaby
Go to the pound and get a cat.

This doesn't always work. I had a cat a few years ago under who the mice would literally hide when they saw me. No joke.