Well, it's high time you learned how it worked. There are Effects that are programmed as apart of the Voice. These are the INSERT EFFECTS.
Then there are a Effects that are applied to VOICES when the Voice is placed in a Part. What's a Part?

When you move to Performance mode, Song mode or Pattern Mode, you place a Voice in a PART. The way to think about this is each VOICE is like a single musician with an instrument. When a musician (VOICE) joins a band (PERFORMANCE) they become one of four members of a four piece ensemble called a Performance.

So the Organ in VOICE mode can have two Insertion Effects. Let's say Distortion Overdrive and a Rotary Speaker. Those are the Organ player's personal Effects. But the band has a mixer so all four instruments of the Performance can be blended (mixed) together. That mixer has two Aux Sends for each player, one feeds a Reverb chamber the other feed a Time Delay effect (Chorus).

A single Guitar Voice might have as its insert effects, a Compressor and an Amp Simulator, these are the personal effects of the guitarist, but when placed in the same Performance as the Organ - each will maintain their own Insert Effects, but they both "share" Send amount controls to the System Reverb and Chorus processors via their individual Aux type Sends.

The Reverb and Chorus blocks are called the System Effects. They recreate the overall environment the music takes place in. Reverberation is something all instruments in the band share... is the band in a small room or a large hall? So in this way all instruments can share the System Effects... where Insert Effects by the nature of how you connect to them are personal Effects.

If you ever played in a band this will be familiar.

When the VOICE is placed in a Song Mixing or Pattern Mixing it is like the individual musician is going to the studio (the Sequencer) is like the multi-track recording studio... there a VOICE becomes one of 16 PARTs in the studio Mixer. Again the individual Voice has its two Insertion Effects and again each has two Aux Sends to the "shared" Reverb and Chorus.

The Insertion Effects are apart of the VOICE
The Reverb/Chorus are called System Effects and belong to the Mixer you plug into as a member of the band.

In the MO-series your favorite three Voices from Voice mode can recall their Dual Insertion Effects from VOICE mode when you are in Performance, Song, or Pattern modes. See page 140-144 of the Owner's Manual for details... about Effects and how they are allocated in each Mode.

You can activate the Insert Effect Switch on any three Parts of a Performance or Song/Pattern Mixing program. These INS SW (Insertion Switches) will determine if you are hearing the Rotary Speaker Effect applied in your program. Make sure the INS SW = On for the Organ Part. Only 3 can be On at any one time, you may have to turn it Off on another Part to set it On on the Part you desire.

[F6] EFFECT
[SF2] INS SW

This should get you started, if you get stuck or have specific questions, post back here in the "Legacy Yamaha Synths" Forum.
Hope that helps.

Thank you for the reply, I will get to work exploring that issue in more detail. Another recurring issue I have is with certain piano sounds. Within a span of no more than one measure, I'll be playing several notes in rapid succession before I let up on the pedal, but the first several notes I play will begin to abruptly cutoff and disappear. What could cause that?

Is there somewhere I could go for an in depth tutorial on the functions of this keyboard?

Another recurring issue I have is with certain piano sounds. Within a span of no more than one measure, I'll be playing several notes in rapid succession before I let up on the pedal, but the first several notes I play will begin to abruptly cutoff and disappear. What could cause that?

The cause for notes cutting off abruptly would be when you exceed the polyphony of the unit. Sustain Pedals on electronic keyboards mimic the reaction of a Sustain pedal on a piano, but accomplish this in an entirely different way.

Each tone that is sounding (and being held by the Sustain pedal counts) uses one note of polyphony. Stereo tones use a Left and a Right tone and therefore count as two notes of polyphony. The MO8 (2005) had 64 Notes of polyphony total, when you exceed this limit Notes will cutoff because there is no tone generator system to support more than 64 tones. (See "Maximum Polyphony" Page 134.

Therefore, careful use of the Sustain pedal is required.

Is it possible to have a loop (such as a pad) playing from the keyboard while still playing in performance mode over the loop (with a piano sound)?

Use an ARP. It's been a while - but in pattern or song mode you can record your own user ARP then use the functions to convert this to an ARP. The somewhat tricky part is that while in song/pattern mode you cannot save this - so your work has an expiration date (meaning when you power off the keyboard) unless you save as a user ARP. You use the JOB function (put track to ARP).

This is coming from memory - so consult the manual for details.

I would then select the ARP in performance mode for the voice which I want to be played in the background behind my "lead" voice.

There are also built-in ARPs which may work.

http://www.cyborgstudio.com/synthmp3s/yamaha/mo6/manual/mo6datalist.pdf

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