I have 4x 328s here.
I can't get ANY of them to work with a three pin resonator or a crystal with two caps.
They only work when I have the two pin crystal plugged in.
If other people have other results, I can't explain the phenomena
It's possible the fuse settings for your 328 chips are set such as not to be proper for the standard oscillator settings. Check out an AVR datasheet for the fuse options offered for oscillator function and if you have the means to read your fuse settings, see if it is set up correctly.
The standard fuse setting for an Aduino 328 are: