Leftover item (5)
(Other definitions for relic that I've seen before include "Revered religious remnant" , "Object from antiquity" , "item of historic interest" , "Object that has survived from the past" , "Object of reverence" .)
'leftover item' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for oddment that I've seen before include "An isolated article, something left over" , "Leftover item" , "a bit spare" , "Just a bit left" , "Left over item" .)