逆(ぎゃく)にOn the contrary

逆に is colloquial, meaning on the contrary or contrary to expectations, often introducing a reversal, as in 応援したのに逆に怒られた (I cheered them on, but on the contrary, they got angry). に反して means contrary to or against, used with rules, intentions, or expectations, as in 規則に反して行動した (He acted against the rules). 逆に can stand alone, while に反して must follow something.

むしろ and 逆に both express contrast, but with different nuances. むしろ presents a preference or clarification, e.g. 話すよりむしろ相手の話を聞きたい ('I'd rather listen than talk'). 逆に highlights an outcome opposite to what was expected, e.g. 喜んでくれると思ったが逆に怒られた ('I thought they'd be happy, but they got mad instead').

却って and 逆に both express something being counter to expectations, like the English 'on the contrary'. 却って is more formal, and occurs primarily in writing in the context of a full sentence or explanation. In contrast, 逆に is quite casual, and can be used in the same way as 却って, but also as an interjection at the beginning of a sentence or phrase, e.g. 逆にたかし君はどう思いますか？ ('On the contrary, what do you think, Takashi?').