Which of the clock sources are actually internal to the ATmega328P? I am trying to determine exactly what all of the fuse settings correspond to on the ATmega328P. The options for the CKSEL bits are:


1111-1000: Low Power Crystal Oscillator 
0111-0110: Full Swing Crystal Oscillator 
0101-0100: Low Frequency Crystal Oscillator 
0011: Internal 128kHz RC Oscillator 
0010: Calibrated Internal RC Oscillator 
0000: External Clock


Clearly, the clocks labeled "internal" are part of the "guts" of the microcontroller. No external components are required to use those clock sources. The external clock is clearly an external source.

My question is this: are the low power, full swing, and low frequency sources built in to the microcontroller itself, or do they require an external crystal oscillator to be purchased and connected to the clock pins? This is not 100% clear from reading the data sheet. (Although I am under the impression that they are not internal to the device.)
If it requires a crystal, as the ones in question clearly state, then obviously you need to connect a crystal (and load capacitors).  Or use a ceramic resonator.

Only those labelled as internal are internal. Everything else is external.