1. Jonathan tripped on down the main street.] Jonathan walked along the main street in a light-footed, good-humoured way. To "trip" is to dance or to skip. Thus in Milton we find: "Come, and trip it as ye go/On the light fantastic toe".
2. His socks had peristalsized themselves] When you swallow a dry piece of food, the regular muscular movements of your throat as you force it down into your stomach constitute "peristalsis". In Self's fanciful phrase, the movement of the socks as they gradually slip down the calf towards the foot are likened to those convulsive movements. It's not an entirely accurate metaphor, as peristalsis usually forces "something else" through a hollow muscular tube; whereas in this instance, it's as if the tube itself has concertina'd.
3. the ungy, sweaty interior of his boots. ] I take "ungy" to be a Self-made word; meaning "gungy", "unlovely", "malodorous" ("humming").
4. the six-legged kine out in force. ] "Kine" is an obsolete plural that means "cows". Here, the insects are likened whimsically to a herd of cows.