They are all very similar but in broad strokes, "scuttle" and "skitter" are more associated with bugs and scuttling is usually a sideways movement, its the way a crab moves. Quite a negative descriptor. "scurry" and "scamper" are more associated with small mammals and the associations aren't so negative. In the latter, "scurry" is associated with fear while "scamper" refers to playfulness. When used in relation to a person, you're comparing or analogizing to the way an animal acts.

This is a personal view on the word, however, the word skitter could also be used for the movement of inanimate objects across each other. I.E. "The small block of ice skittered across the hot frying pan" or "The stylus skittered across the record".

No double letters right? XD