Error using nRF24L01+ with ATmega328P-PU. Works fine on Uno
The ATmega328P can't run at 16MHz at a supply voltage of only 3.3V (check the datasheet). Either raise the voltage or lower the frequency.  

Also note that 16mHz would be 16 milliherz (16E-3), so you probably mean 16MHz, i.e. 16 megahertz (16E6).

Remember that the nRF24L01+ is a 3.3V device, so don't connect it to the ATmega's Vcc when changing the supply voltage to 5V.
The IO pins are 5V tolerant, so that's not an issue.