You are correct in that the digital input is only 1 of 3 options at one time: AES, Spidf (the RCA/Coax jacks), or Optical Spidf.
After you've configured what you want in the mixer, your only real choice if you want to stay digital and have both things hooked up at the same time would be to go in the hardware setup, under the "main" tab, and click the button from spidf to optical spidf or vice versa, depending on what you want to hear. Kind of a pain though.
The other option would be to not try to use the digital out of your computer, but rather just the analog line out, into analog line in 3-4 of your Omni, and then keep your POD HD hooked up digitally.
Regardless of what you choose, the mixer function is pretty easy to use. It's just like a regular hardware mixer built into your Omni.
Assuming you're using stereo pairs, choose whichever stereo pair of inputs you want (you can choose more than one), and click on the "MON" button for each channel of the stereo pair, both left and right. Also click the "HP" button to hear stuff through the headphones as well as your monitors.
VERY IMPORTANT: Make sure that the Pan sliders at the top are panned all the way to the left and right, respectively, if you want to hear your stereo sources in stereo. If you're using a mono source, like for example using the mixer function to plug in a bass guitar to the DI of channel 1 just to play without opening Protools, then you may want to keep the Pan slider in the center, so it will come through in the center just like it was a mono track in Protools panned to the center.
So in your scenario, by enabling various channels in the mixer tab, you could have your computer analog line out to analog 3-4, and your POD HD into the digital in, and bass or guitar plugged into channel 1, and you could hear them all at any time, in fact all at the same time, whether Protools is open or not. You could even have your computer shut off and the Omni disconnected from the HD Native card, and still hear them through the Omni and your monitors, just like a hardware mixer.
Lastly, at the bottom of the mixer tab it says "record/input monitor enable", and gives a choice of "Mutes Mixer Input" or "Ignore (manually manage mutes)".
You will most likely want to choose "Mutes Mixer Input", that way when you go to record with your POD HD, and record enable it, or click input monitoring, you'll just hear it the normal way coming through Protools, at whatever buffer setting you've chosen. Otherwise, you might hear both the signal going through Protools and the same signal coming direct through the mixer function, and be hearing the same thing twice, slightly off in timing.