Outside of the Middle East, it would be fair to assume that the pre-eminent exponent of the oud would be the redoubtable David Lindley.

An interesting snippet from his road journal reads as follows

Figured out the Buck Owens/Don Rich instrumental tune "Buckeroo" on the oud in harmony parts, two parts at once like two guitars. It sounds pretty good too.

Personally, I am not in the least interested in the oud, but I am sure that Mr Dave will answer any questions you might care to put to him if you visit his website
http://www.davidlindley.com

He is very approachable, I have corresponded with him before.