Cheap cigar goes with it, oddly (6)
I believe the answer is:
stogie
'cheap cigar' is the definition.
(I've seen this before)
'goes with it oddly' is the wordplay.
'with' means one lot of letters go next to another.
'oddly' is an anagram indicator.
'goes'+'it'='goesit'
'goesit' with letters rearranged gives 'STOGIE'.
(Other definitions for stogie that I've seen before include "Long thin inexpensive American cigar" , "Egoist (anag) - cheap cigar" .)