The alphabet goes from A-Z, but I go from Z-A. What am I?

There's nothing on draught when I show off my bars. Nothing hair to comb when I show off my locks. I can house rodents, I can house birds. I may be quite fancy or just the shape of a box.

One: You gotta hit me on the head, literally and figuratively, for me to be effective. Two: Bite me to appear nervous or paint me to appear well put together. Three: Use me as a colloquial way to celebrate an achievement.

sweet as can be, you'll have to undress me

The Liberty type has one e, the Southern type has two. If you change the e in the Liberty type to an a, it is where you might find the Southern type.