Here is another way to look at it.

 

I don't understand why that's 0 volts though since there's an input there. Why doesn't the first L input under the junction with the switch, cause a voltage to appear there between your mono label and its resistor on the upper set?

[EDIT] I see your latest post, I was typing as you posted apparently. But the same question remains to me.

 

The major point is that no matter what you connect to the inputs, the negative input pin of the op amp will be at zero volts. The right side of all the input resistors is at zero volts. That's what the op amp does. It nulls the input. Whatever voltage you connect to an input resistor will cause the op amp to react by making the negative input pin zero volts. The op amp does this by outputting the negative of anything you put in the input. When they meet at the negative input pin, they cancel.

 

Ok, so I guess in the most basic sense, I guess this is a little like connecting something to the 0v side of a resistor in series with a voltage source. Maybe not technically correct, but now it's starting to make more sense, and there's probably a better analogy. I shall try your latest schematic as soon as I can!
Thanks!

 

It's called, "virtual ground". The positive input is grounded so the op amp will do anything in its power to keep the negative input at zero volts. Anything you put into an input resistor will disappear. Only the output of the op amp has a reflection of the inputs, and that is the inputs times negative one. The two op amps on the right only flip the signal back right side up.

 

First of all, thank you so much #12 for all the help. There is indeed no crosstalk on the other channels when the switch is thrown. I still don't quite understand it, but I'll go with it for now.

Unfortunately, I have one more question. I'm currently using the LM324 chip which of course was recommended against earlier, I'm planning to upgrade to the TL074 or NE5532 as mentioned, but have a slight problem. Both of those want a positive and negative supply voltage which I don't even have. I've seen designs online that make interesting use of voltage dividers to give what I guess is a virtual ground (midpoint) on the noninverting input, but they still require two different voltages, maybe +6 and +12 instead of +/-12, but I'm going for simplicity here. I've also seen postings that say you can just go ahead and drive these chips with a single positive supply. Which should I believe? I'd really like to eventually power this from a single 5v source (ok, I'll admit it, USB) but for now I'm satisfied with a 9v battery, hopefully just one. Can anybody point me in the right direction? Or better yet, a single-supply chip with the same better audio characteristics of the TL074 or NE5532 vs the LM324?

I'm sorry for all these questions for this one simple project. Unfortunately, I'm only good in electronics through basic diode use, anything more complicated such as this, and I get lost quickly.
Thanks!