The most common and most likely answer to this crossword clue is the 8 letter word PECULIAR
I've seen this crossword clue in Independent
P
E
C
U
L
I
A
R
More clues leading to the result PECULIAR
- Training copper who tells lies: strange
- Poorly / individual
- One's own special rum
- Particular metallic elements in fruit
- . Bizarre to see police on vacation with copper and perjurer
- Strange individual
- Unconventional characteristic
- Bizarre muddle I clear up
- Odd fruit seen around to pick off with fifty taken by Crosophile
- Odd clue I more than half parse wrongly
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 = peculiar.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.
What does PECULIAR mean?
PECULIAR noun- That which is peculiar; a sole or exclusive property; a prerogative; a characteristic.
- (canon law) an ecclesiastical district, parish, chapel or church outside the jurisdiction of the bishop of the diocese in which it is situated.
- Out of the ordinary; odd; strange; unusual.
- Common or usual for a certain place or circumstance; specific or particular.
- One's own; belonging solely or especially to an individual; not shared or possessed by others.
- Particular; individual; special; appropriate.