In Mark when Jesus is being tempted in the wilderness, He was up against Satan and wild beasts.
The birds of the air that devour fleshly planted seeds in the sowing of the word parable I believe are demons.
In Revelation 18 bound in the prison are Satan, and birds, and demons. (Forgive me I do not have my Bible in hand, am drawing from memory).
I encounter phrases about birds and beasts frequently that I believe are demons, it makes it interesting to read these references in this light.
In the Books of the Prophets in the OT, one of God's judements is to leave people out in an open field and let the wild beasts and birds devour them (therefore there is no hedge of protection--open field--from these powers of the darkness), or will put cities to ruins and allow the birds and beasts to reside there.
The tree in Nebuchenezzar's dream in Daniel had birds of the air nesting and beasts of the field in it's shade.
I agree that by no means all of the references to birds or beasts are speaking of demons, but many do.