Feel, hear, see, smell, and taste are Sense Verbs. They refer to the actual, physical, physiological senses of touch, hearing, sight, smell, and taste (which are mostly derived from these verbs). Sense is a generic term referring to all or any of the above, um, senses. These are basic words.
However, all of the senses are involved with emotions; it is a truth universally acknowledged that some things look, sound, taste, smell, or feel much better than others -- and vice versa -- and they can provoke all sorts of emotions. So sense verbs are used constantly as metaphors for the mind, including the emotions. Remember the blind men and the elephant?
- The whole proposal looks a little shaky to me.
- The whole proposal feels a little slimy to me.
- The whole proposal smells a little rotten to me.
- The whole proposal sounds a little crazy to me.
- From the proposal, I sense that he wants a little taste of the leisure life.
Since sense is general, it's often used for purported "Extra-sensory perception", or intuition, or other, even less well-defined, um, "sensations".
- I experience a deep sense of peace whenever I touch the gong.
- I sensed immediately that they were nervous.
- Do you sense a shift in their bargaining position here?