I have posted advice over the years about evicting squirrels. Since right about now seems to be a peak time for squirrels squatting in owl boxes, I thought I'd try again with a summary of techniques I've learned.
1. Most important: Evict the squirrel and get rid of all the leaves he has crammed in there. If you see a squirrel bringing leaves into the box, wait till the end of the day and then clean out the box. Rinse and repeat, weekly if necessary.
2. If the squirrel is in the nest box when you want to clean out the nesting materials, bring a long stick with you and whack the box. Nothing like surprising him and forcing him to leave in a hurry to make a big impression.
3. I hate to say it, but take down your bird feeder if it's anywhere near the owl box. Like chipmunks, squirrels like to live near easy access to food.
In summary: Make life as difficult s you can for the squirrel. He can live anywhere. Screech Owls need nesting cavities more than he does.