The most common and most likely answer to this crossword clue is the 9 plus 1 letter word EDGEWAYS} –
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Buddy explains!

The straight part
We know that "obliquely" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obliquely = edgeways} –.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 EDGEWAYS} – mean?
EDGEWAYS} – adjective- With the edge facing in the direction of movement.
- With the edge uppermost.
- With the edge facing in the direction of movement.
- With the edge uppermost.
- A form of railway in which the road is causewayed up to the level of the top of the flanges.