Keep all food in tightly shut containers with weights on top, making sure there's no crumbs on the ground overnight.
Consider trying Mouse Magic by Bonide - it is a nontoxic repellent of peppermint and spearmint - mice supposedly hate it and also cotton balls dunked in peppermint oil. I would not put these things directly where your feathered friends sleep in case the smells bother them. Place in other areas nearby and hopefully the mice will leave the premises. It did work for me and for a friend of mine who had mice taking up residence in her car engine.
Hav-a-harts do seem to work great for harmlessly catching mice so long as the bait is tasty. You can then choose to release them if you wish away from people at the edge of woods and a field setting so they can find the food they need. Don't beat me up people - I will never kill if there is a reasonable alternative.
I would never use glue traps - they are cruel and medieval. Long suffering and terror when a being gets stuck to those things. I would also never use poison - indiscriminate - there are often unintended victims.
I understand the frustration and dilemma - been there, done that but it all worked out - good luck.
JJ