I have a 14/2 (one circuit) and a 14/3 (two circuits), both Romex NM, coming into a regular steel handy box (2x4") and continuing on from there via outdoor cables (UF cable ?). Am I compliant with the NEC, considering it's three circuits and a total of 6 capped splices? It all fits in but you couldn't fit a smidge more.
Short answer is you are way undersized on your box and it does not meet the National Electrical Code. Here's why:
Table 314.16(A) of the NEC does not list handyboxes for sizing but I am going to estimate they are the same size as a standard devices box of 2" deep. That would probably be generous. So, that would be about 10 cubic inches volume. The table says you can put 5 #14 wires in them. However, the code requires you to count each wire entering a box from outside once so when you make a splice it gets counted twice (314.16(B)(1)).
So, your example would be 10 wires total (5 in and 5 out) plus the ground for 11 wires (the grounds only get counted once no matter how many you have (314.16(B)(1)). Table 314.16(B) shows #14 wire needs 2.00 cubic inches per wire so you would need a box of 22 cubic inches.
Back to Table 314.16(A) and you would need a 4" square box 2 ⅛" deep or a 4 11/16" 1 ¼" deep box.