Hi, Jayanem,
On behalf of the Admin and Moderator staff at BirdForum, a warm welcome to you!
You mention "birdfeeder" in the singular. Can you tell us what kind of feeder you have, as in what its shape is? And what kind of feed you're using?
In my own yard, I keep larger seeds/nuts separate from the smaller seed that the smaller birds favor. This keeps the jays/woodpeckers, etc., from not only competing with the smaller birds for food, but even keeps them from being in the same physical area.
I'm sure someone else will be able to better address your problem for you, but I wonder if putting up another feeder with larger seeds would draw the woodpeckers away from the smaller birds? Also, providing feed that only woodpeckers (and nuthatches) can access, such as smearing crunchy peanut butter on the bark of trees, or hanging a suet cake on a tree in another part of your yard, will attract the woodpeckers and maybe keep them interested enough they'll leave the other feeder alone.
Some folks like to put a wire mesh enclosure around their small-bird feeders. The outer wire mesh allows small birds to get in but the larger ones can't fit. Unfortunatley, this keeps out ALL larger birds, not just the aggressive woodpeckers.
Hope this helps!