Poem, while oddly cheery, funny (8)
I believe the answer is:
clerihew
'poem' is the definition.
(clerihew is a kind of poem)
'while oddly cheery funny' is the wordplay.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
'funny' indicates anagramming the letters.
The alternating letters of 'cheery' are 'cer'.
'while'+'cer'='whilecer'
'whilecer' with letters rearranged gives 'CLERIHEW'.
(Other definitions for clerihew that I've seen before include "Humorous verse form" , "few personal lines" , "Two-lined comic verse" , "Funny lines" , "Bentley's jingle" .)