As you have found out, starlings can be a problem. They compete with native species for food and housing and most of the time will hog everything. What kinds of feed are you offering? Maybe that is what is attracting them. When nesting season begins they might try competing for any boxes you have, whether they can enter them or not. I don’t know how you feel about trapping them but it can be done. In any case, those starlings have to go!