What size device box should I use with 3-16/3 cabels insulated one bare ground, one switch, grounding wire and three cable clamps?

First, you should not be using wiring smaller than 14 gauge (as the gauge # gets bigger the wire size gets smaller). 14 gauge and 12 gauge are the most common sizes you'll find in houses

If you refer to the National Electric Code, table 314.16(A), that will give you the answer. Assuming you have 14/3 cables, the table tells you to use a 4" square box that is 2 1/8" deep.