software

So if your playing a combo and you want it to run into a speaker cabinet, say 4x12...

Do you have to disconnect the combo's speaker? What if the speaker and cabinet both run at 4 Ohms (or both at 16, or both at 8).

Can you run both the cab and combo's speakers, or must you disconnect the combo's speakers, thus essentially converting it to an amp head?

Without getting into the math involving proper ohm ratings, use them both. I do. Two eight ohm speakers, each delivering a 4 ohm load to the amp.

depends

if both are 4, and the amp was designed for 4, it's borderline safe total of 2 ohms.

What you could do is wire the internal speakers in series for 16 ohms, then run them with the 4 ohm 4x12 in parallel for a total of 3.2 ohms, which is still safe, uses some power through the internal speakers, but focuses on the 4x12.

Rereading your question, I assume that you are asking about how to make a rating judgement. What do you have, and how are they rated?

What about stereo inputs each rated at 8 ohms...two combo amp speakers each individually rated at 8 ohms...

The notion is that JC-120s behave like two separate amps (stereo), so the ext. speaker jacks are like two different amps running at 8 ohms.

My cabinet just so happens to have a selector for 4/16 ohms mono, 8 ohms per side stereo.

My thought would be that each side being 8 ohm 8 ohm = 4 ohm/stereo setting on the cabinet, but I can't tell enough from the owners manual for the amp to be sure that the amp is wired that way.

Well I run a Marshall quad from my Peavey Bandit combo's ext. speaker jack, but with the speaker disconnected. I couldn't stand the sound of the Peavey speaker at the same time as the Marshalls. It works either way, but if you disconnect the combo speaker, NEVER turn the amp on without having the ext. cab plugged in! Sorry I can't help about the stereo issues though!