。
She gave me a strange look.
Literal
She [topic-は] me [object-を] strange eyes [with-で] looked-at.
The productive frame [adjective] + 目で見る builds a charged look from whatever adjective sits before 目, leaving 見る itself plain. Here 変な ('strange, weird, off-putting') gives the look its uncomfortable quality — the kind of glance you'd get for saying something out of place or behaving oddly. 変 is a な-adjective; the な before 目 is the standard linker between na-adjective and noun. Other adjectives slot into the same template (優しい目で 'tenderly,' 厳しい目で 'sternly,' 疑いの目で 'suspiciously').