First off, congrats on the nice equipment, particularly the receiver!
If you're only seeing Pro-Logic II or Neo:6 that means your receiver is getting a stereo signal.
Regarding "Are the DD and DTS modes only displayed when you have a DTS or DD source?" that is correct, you will not be able to select said modes unless the onkyo is getting the digital signal.
One quick recommendation, right click on your speaker icon in your OS (what are you running?) click on the signal you're using (the SPDIF) and then hit configure, or something similar depending on the OS, then you should be able to pick between 2 channel and 5.1 or 7.1. Pick the correct signal, hit next, next, and you should be good to go.
Let me know if the above makes sense, we'll get it figured out!
Seth