What do you mean by “swing crystal”? There are ‘standard’ two pin crystal oscillators, and then there are three pin ceramic resonators. 328p16m just expects a to a 16Mhz oscilator… whether it be a crystal with load capacitors, or a three pin ceramic resonator.
A minimum, your circuit should have a 10K pullup to V+. Something like a 100nF capacitor on V+ and GND near the atmega328 pins would be good, but not critical. Also, don’t forget to put load capacitors between the crystal and ground! And probably a good idea to also connect the analog V+ and GND pins also…
