She looks odd when she wears that kimono.

Literal

She [topic-は] that kimono [object-を] wear [when-と] strangely appears.

~と here is the conditional 'when/whenever' — wearing the kimono reliably triggers the strange appearance. 変に見える ('look strange') uses the adverbial form of 変 (a na-adjective) plus 見える ('appear'): the same pattern as 大きく見える ('look big') except that na-adjectives take ~に rather than ~く for adverbial form. 着物 is a fitted traditional garment — what looks odd on someone might depend on their stature, the kimono's pattern or formality level, or the occasion. Note that 着物 specifically refers to the traditional Japanese garment in modern usage, though the kanji literally just mean 'wearing thing.'