The most common and most likely answer to this crossword clue is the 7 letter word WHIMSEY
I've seen this crossword clue in The Times
W
H
I
M
S
E
Y
Buddy explains!

The straight part
We know that "Odd" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case odd = whimsey.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
WHIMSEY noun- A quaint and fanciful idea; a whim; playfully odd behaviour.
- An impulsive, illogical or capricious character.
- A whim (capstan or vertical drum).
- A jigsaw puzzle piece that has been cut into a recognizable shape, as if on a whim; often the shape is representative of the theme of the image used for the puzzle.