Hey, I still have the wimpier little brother of this mixer, the Tascam M-30.
The reason it doesn't make easy sense to our new millenium eyes is that this mixer is sort of a hybrid of studio and live mixers. Back when this product was sold, Tascam was selling a lot of small 8-track recorders that recorded on 1/2 tape (open-reel 8-track, not car 8-track!). Reading that may have just triggered flashbacks for some of us, as we remember a world with big reels of tape turning, lots of time cleaning recording heads and rollers, and where you couldn't cut and paste takes together on your laptop! Hey, it was legendary that the Eurythmics demo tape was made on a Tascam 80-8! You can bitch about how much ProTools costs now, but the gulf to professional recording equipment was endless just 15-20 years ago.
The idea behind your board was to create an environment where you could record multi-mic setups into an 8-track recorder, then mix that 8-track tape down to a stereo master without having to use a lot of external mixers or repatching.
A 8-track recorder doesn't have enough tracks for you to capture each drum mike independently, so what you did back in the day was put the kick drum on one channel and mix everything else into a stereo pair. If you had 6 drum mikes, you plug those into your regular channel strips and use the bus assignment switches to create a the stereo drum pair on an even and odd buss which you then route to two channels on your recorder (actually, doing this takes a patchbay on my board, but yours might be able to do it directly). This is why you have that even/odd panpot.
After you got your tracks recorded, you use hit the line button on the channels that the recorder is connected to (usually 1-8) and you can do the stereo master mix from there. In addition to the simple effects send on each channel strip, you can use the buss routing now as effects loops for each group in mixdown (OK, more patching going on here).
The Aux busses were intended for your player's monitor mix. My wimpier model had only one aux buss and a separate 8-track monitor mix, which I don't think yours has.
Above the buss 1-4 sliders, it looks like there's two sets of input controls. I'd be curious what the legends are on the lower sets of knobs. Perhaps those busses are stereo instead of mono (like mine). If so, that's probably what that orange L-R button is doing.
The idea behind these mixers was to set the thing up so that it was effectively pre-patched close to something useful for non-pro recording. With a traditional board you had more flexibility but had to patch every connection which meant lots of patchbays and cables (not only dollars there but brain capacity to understand what you were doing). Doing it this way helped the basic user out in getting tracks recorded and mixed down. This kind of mixer sort of became a dinosaur by the time the ADAT came around (early 90s) and there started to be a lot more channels around to route. I don't think we're quiet at a point yet where artists on the radio have never used anything other that ProTools, but I think we'll probably hit that in less than 5 years.
Have fun. I don't know about your mixer, but the smaller M-30 had a wooden case and wasn't something you'd travel with.
David Fung