It’s not just eagles that are federally protected – all native birds (and bird parts, including feathers) are protected under the Migratory Bird Treaty Act of 1918. Most of the time you won’t get in trouble for having a few feathers, but just be aware that technically you could get fined for having any bird parts without a permit.
Starlings, pigeons, house sparrows and other non-native bird species are not protected in this way.
I totally understand your roadkill thing – I currently have a really cool raccoon skull sitting on my desk that I found on the side of the road. It was really well picked over by the time I found it, and just had a few wisps of hair clinging to it.
My recommendations: be careful and use gloves if it is fresh, especially with mammals, and maybe leave it in a safe place for “nature” (i.e., burrowing beetle & other insects) to clean it up for you. For example, if you wanted a fox skull from a road kill, you could stick it in a wire cage outside so scavengers can’t drag it away or destroy the skull but insects can clean the flesh off for you.
Okay I’ve probably grossed-out everyone on this site by now…