The most common and most likely answer to this crossword clue is the 7 letter word RUMMEST
I've seen this crossword clue in The Guardian
R
U
M
M
E
S
T
More clues leading to the result RUMMEST
Buddy explains!

The straight part
We know that "most odd" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most odd = rummest.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 RUMMEST mean?
RUMMEST adjective- Fine, excellent, valuable.
- Strange, peculiar.