The most common and most likely answer to this crossword clue is the 7 letter word OFFBEAT
I've seen this crossword clue in The Times
O
F
F
B
E
A
T
More clues leading to the result OFFBEAT
- High pulse is weirdly unusual
- Bizarre situation of constable doing desk job
- Unusual of female to attend
- Strange being away from work with strike
- Not on strike? That's unusual!
- Like PC in office, say, not performing as expected
- Funny like Bobby after work?
- Unusual puzzle disappointing at first
- Oddball to attend on officer
- Eccentric, like policeman who has finished duty?
Buddy explains!

The straight part
We know that "weirdly unusual" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case weirdly unusual = offbeat.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 OFFBEAT mean?
OFFBEAT noun- The beats not normally accented in a measure.
- An unconventional person, someone who does not follow the beat, who chooses not to conform.
- Unusual; unconventional; not ordinary.