The API is open to any language since it answers HTTP calls.
http://developer.vimeo.com/apis/simple
if you need to show private videos , you need to use the advanced API, and this is a little more complicated, since it is more secure. The advanced API uses OAuth 1.0 for authentication.
http://developer.vimeo.com/apis/advanced
What you probably want to know is the availability of the Android Wrapper for the Vimeo API , but I don't know anyone , but as said, these are simple calls that you send JSON or XML objects , and if you use the advanced API, to handle authentication there are many libraries .