I don't have the time to reply to everything in detail (I might come back later, but I'm not an expert at the high-end audio settings), but... For Audio Out, you'll probably have the best results with WASAPI (either Event Style or Regular, whichever works right with your hardware/drivers) if ASIO doesn't work right (common with consumer cards like the Xonar). WASAPI is bit-perfect when in exclusive mode (the default), so the drivers and or Windows won't get in the way and mess with your audio output. This should work with the Xonar. Try it out.
Direct Sound and Wave Out are both NOT bit-perfect settings. They go through the "normal" Windows sound system.
JRSS is a very high-quality and flexible up/down-mixing system, similar to Dolby Pro Logic or DTS Neo 6, but with far more capabilities. Primarily, it is used to expand stereo sound to 5.1 or 7.1 (or whatever) surround sound. So, if enabled and set to 5.1 channels, it will upmix your stereo music to surround. However, one other handy use for it is to downmix multichannel sound (like Dolby Digital or DTS-MA) from a DVD/BluRay/MKV/MP4/whatever to a smaller set of channels (like 2.0 or 2.1). This is handy because normally if you play a video with AC3 5.1 audio on a system that only has stereo outs, you can miss a LOT of the audio, particularly the center channel (which can make it hard to hear dialog).
JRSS has a sophisticated system for mixing these things up and down, without otherwise corrupting the audio (and Matt puts particular care into ensuring that it doesn't cause the channels to clip or needlessly distort). The audio path inside MC is fully 64-bit, so this processing can be done with a very high degree of fidelity.
I, personally, find that it does an AMAZING job upmixing stereo music to 5.1 surround. For movies, I can't decide if I like JRSS better or the DTS Neo 6 setting on my receiver better, and I keep switching back and forth (JRSS is easily superior to ProLogic's default settings in my opinion). Otherwise, for video playback, if you are going to just be connected via SPDIF, you'll want to enable Bitstreaming under Options -> Video (if you are connected via HDMI, it is debatable whether you should bitstream or not, but for SPDIF, you almost certainly do want to bitstream video tracks when possible).
Depending on your settings, you can enable it for JUST music, or for both music and video (the default):
If you want to enable JRSS for everything, just enable it in the DSP and it'll automatically work when you play a video back with only stereo audio.
If you want to enable JRSS for music only, and let the receiver deal with expanding stereo audio for video content, then set Options -> Video -> Advanced -> Audio Playback device to point directly to your Xonar, rather than the default "same as audio" setting.