a half woman and a half bird in the Odyssey is called a Siren.
Half human-half dog is called a youkai. half human-half fox is called kitsune
A half fairy and half human is typically referred to as a "half-faerie" or "half-fey".
Nephilim
Fae.
No bird can be described as half bird/half mammal. The Duck Billed Platypus was thought to be a "mixture" of animal types when it was first discovered, but the "bill" is unlike a true bird's bill.
There is no fantasy creature that is half horse half human and NOT called a centaur.
Are you sure you're not talking about a flying squirrel? They don't fly, but they glide. I don't think there is such thing as a half bird, half squirrel. If there is, combine bird and squirrel. (Squird or Birrel or something)
it is a centaurs
A Sphinx
hermaphrodite
A "werewolf".