Lay out odd parts of diet: odd bits of cake (4)
I believe the answer is:
deck
'lay out' is the definition.
(I've seen this in another clue)
'odd parts of diet odd bits of cake' is the wordplay.
'odd parts of' indicates alternate letters (letters in odd-numbered positions).
'odd bits of' indicates alternate letters.
The alternating letters of 'diet' are 'de'.
The alternating letters of 'cake' are 'ck'.
'de'+'ck'='DECK'
(Other definitions for deck that I've seen before include "Pack - floor in boat" , "Pack of cards (US)" , "Set of cards" , "Horizontal floor on a ship" , "Pack - embellish - ship's floor" .)