Looks like you have been discovered by the local predators and they bringing all there friends to check you out. Based on the photos and what you have described, you need to go Ft Knox on them and if it's real bad, start running traps 24/7. (It doesn't cost any more to occationally trap vs having one a set running all the time in various spots)
You need to lay a heavy wire skirt around the coop and run about 24" wide. Be sure to attach the inside edge to the base of your run to prevent the critters from simply pulling it away and stake it down flat if needed. If you have a minature hand print type track, you should consider wiring the top or look into premade chainlink kennel panels if they are the right size. Otherwise you should get in the habit of locking up your birds in a secure coop at night.