What is nyctinasty?

Nyctinasty refers tothe nastic movement of leaves or petals of higher plants in response to darkness(or the alternation of day and night). The closing of a flower at dusk, for instance, is a biological rhythmic event. It is a biological rhythm since this behavior recurs in each circadian day.

Nyctinasty movement is the rhythmic nastic movement of plant in response to the onset of darkness. It is also called as sleep movement. Drooping of legume leaves in dark is due to nyctinasty. Mimosa...

What is the term for the sleep movement of leaves of leguminous plants?

The term  is Nyctinastic movement. It is induced response  to diffused stimulus  i.e. light or temperature. 

If you touch the leaves of Mimosa pudica, it folds and wilts. What kind of movement is this?

This is seismonastic movement.    Here,  the plant respond   to diffused stimulus i.e.  our  touch  or shock .