Need 1-4 pins controlling 16pins logic level
The easiest way is to use one 16 bit shift register (or two 8 bit shift registers connected together). That would require only 3 pins.


Data
Clock
Output latch


You would need a 16 bit variable where you set or clear the bits, then you shift the data through the shift register, and then activate the output latch.

You can use two 74HCT595