I was watching Lonesome Dove this weekend [love that movie] and one of the charactor’s was talking to someone about taking off their clothes, but instead of saying “take off your clothes…” he said, “Strip off them Duds…” My question is easy…what are Duds and where did the word come from?
Duds are clothes. The word comes from Middle English “dudde” which seems to mean a cloak.
Duds are, as you’ve guessed, clothes. From Etymology Online:
Cool, glad the westerners of old were holding onto some old world traditonal phrases. 
A lot of regional dialects in America were remnants / descendants of old world regional speech. I had a teacher once who had done extensive reasearch into the legacy of the Southern dialect, a lot of Scottish influence if I remember correctly.
“Duds” is slang for underpants in the area surrounding Wigan (probably elsewhere, too).
I used to live across the street from a laundromat named Suds Yer Duds. In American, “Duds” mean any kind of clothes.