Odd graduates soaked sponge (3,4)
I believe the answer is:
rum baba
'soaked sponge' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'odd graduates' is the wordplay.
'odd' becomes 'rum' (rum can mean strange or dubious).
'graduates' becomes 'baba' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'rum'+'baba'='RUM BABA'
Can you help me to learn more?
(Other definitions for rum baba that I've seen before include "Spirit-soaked sponge" , "Spirit-soaked cake" , "Rich cake" , "Soaked sponge dessert" , "Sweet" .)