That's most of the positions. If its wings are inverted , the wing tips are turned down. Remember that when we were talking about four legged animals, addorsed meant back to back. Now, you don't have to have a eagle, hawk or falcon. You could have any bird you like.
Some birds have some particular default positions as well.
The head still faces to dexter. The default for an owl is close, head affronty. Swans can be depicted in all the usual positions, but because swans swim, they are often shown this way. The most common bird shown in the SCA would have to be the pelican , which does not look much like a natural pelican at all. It cannot be used by anyone in the Society who is not a member of the Order.