Odd wings of migratory game (5)
I believe the answer is:
rummy
'game' is the definition.
(rummy is a kind of game)
'odd wings of migratory' is the wordplay.
'odd' becomes 'rum' (rum can mean strange or dubious).
'wings of' says to hollow out the word (remove centre letters) (letters on the two wings removed).
'migratory' with its middle removed is 'my'.
'rum'+'my'='RUMMY'
(Other definitions for rummy that I've seen before include "Peculiar - card game" , "Two-pack card game" , "Set, sequence card game" , "Odd; card-game" , "game of cards" .)