Simple mouse trap works wonders. I don't like using glue traps because it's inhumane, but they can catch mice along with some pretty big insects. Snap trap or a zap trap (careful of fire) works best, I set them up during the day when the chickens are NOT in the coop. Wash your hands after emptying the mouse from the trap. No point in relocating the mice because it will just find its way back to your coop.
Eliminate sources of food and store the feed in barrels and trash cans. With gloves on, wipe down and clean surfaces with mouse feces on them and make sure you wash your hands. Dedicate one N95 mask to wear when cleaning the coop, hantavirus is caused from inhaling dust with little particles from the mice. You can reuse N95s over and over. If you don't have one, wear a scarf or bandana, but I can't guarantee protection.
Whenever I find mouse poop I use old laundry detergent powder and water to clean it. Don't really need anything beyond simple soap.
After everything's all said and done clear up unneccessary brush and grass from near the coop to prevent them from gathering nesting material and cover the holes.
Chickens shouldn't be attacked by mice, usually they're the ones who chase down and eat mice. But I lost one pullet to a large rat. If they are rats you're going to need a bigger trap.