First, I'm assuming that the speakers you show have their own power and amplification, so that throughout your schematic we're dealing with low-level audio signals, right? Ie: you're not hoping that the PC output will drive raw speakers?
Assuming this is correct, your schematic looks like it does what you describe, but here's a thought. As you have it wired, you are committed to using only the speakers or the headphones, but not both at once. You couldn't listen to the ipod on the headphones while the PC sends its sound to the speakers, for example.
Instead, consider wiring up two parallel "copies" of SW1, where the output of one of the "SW1"s is wired direct to the speakers (possibly through a jack) and the other "SW1" has its output direct to the headphones. Essentially these SW1s function as input selectors for the speakers and headphones respectively. It won't be a problem if both select to listen to the PC, or both the ipod.
As for driving LEDs off the audio signal, this will not be satisfactory. An LED needs at least 1.4 to 2V to illuminate, which your audio will be below much of the time. In addition, when lit the LED will draw more current than the low level audio signal can provide (without distorting the signal a lot).
You might consider replacing the DPDT switches with DP-3-throw switches, and use the extra throw to control LEDs. You could conveniently get power from the computer USB jack. Use 150 to 300 ohm resistor in series with the LED to operate off 5V -- adjust to suit your taste for brightness.