却(かえ)ってAll the more, On the contrary, Conversely

Both introduce unexpected outcomes, but differ in type of surprise. 却って means the result was the opposite of what was intended or expected, e.g. 謝ったら却って怒られた ('When I apologized, I was yelled at instead.') ところが highlights a surprising turn of events, though not necessarily the exact opposite, e.g. 田中さんに電話をかけた。ところがもう出発していた ('I called Tanaka. But he had already departed.')

Both むしろ and 却って express contrast with expectation, but differ in nuance. むしろ introduces a preferred or clearer option, e.g. ワインよりむしろビールが飲みたい ('Rather than wine, I'd rather drink beer'). 却って highlights ironic reversal, e.g. 手伝ってあげたのに却って怒られた ('I helped, but they got angry 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?').

Both convey contradiction, but they differ in usage and nuance. 却って connects to the rest of the sentence to emphasize unexpected results, e.g. 慌てて出ようとしたら、却って遅くなった ('I tried to rush out, and I actually ended up running later.'). In contrast, に反して connects to a noun and highlights going against norms or expectations, e.g. 親の期待に反して、大学に進学しなかった ('Against his parents' expectations, he didn't go to college.').