Cloth scrap (3)
'cloth scrap' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for rag that I've seen before include "organ?" , "Tattered cloth or university fiesta" , "Piece of cloth for student's fun" , "This trade is the clothing business" , "Tattered cloth or university romp" .)
(Other definitions for oddment that I've seen before include "Remnant" , "Scrap" , "Leftover item" , "Curiosity, peculiarity" , "Leftover piece" .)