He tilted his head quizzically as he looked at her.
He gave her a side-long glance.
That picture is slightly askew.
ご質問ありがとうございます。
小説作家の言葉使いは,結構緩やかだと思うけどちゃんと答えてみます。「askew」は「斜交い」という意味です。例えば:
Don’t you think that picture is slightly askew?
あの絵はちょっと斜交いと思わないの
「He looks askew at her」は「頭を傾げること – tilt」と言う意味と思います。たとえば:
He tilted his head quizzically as he looked at her.
及び
He gave her a quizzical tilt of his head.
「Quizzical」は「物問いたげ」という意味です。
Bonus Point!
「skew-whiff」はイギリスの英語で「askew」と同じ意味です。例えば:
Your hair is all skew-whiff!