感じ - most often used in regards of "feeling" and the one I myself use the most often to express that I have a good or maybe strange feeling about something, but also to express that a sweater has a good feeling on your skin, and so on
感覚 - sensory perception/ sensation that can also be used as "intuition" and not as a physical feeling
気持ち - used to desribe a situation related feeling, like "feeling good/comfortable" (気持ちいい) or that you don't feel well (気持ち悪い) because of maybe something bad you ate
気分 - is used mainly to express your mood or how you feel physically (eg. 気分はどうですか。)