Someone with a greater understanding could probably explain things better, but here's my simple breakdown of the multi-coil setup:
Jazz pickups are single coils around a single bobbin which sense a small area of the strings vibrations giving a bright and clear sound that is susceptible to hum.
P pickups use a split coil (the E&A strings have one coil and the D&G another each with their own bobbin) which means a larger midrange emphasis and a slightly muted top end. The two coils are humcancelling as well.
The Wal pickups actually use two coils PER string so a total of 8 separate bobbins (10 on a five string) which create a very distinct sound. I believe each row of coils (all the ones toward the bridge for instance) is summed in series and then the two sets summed in parallel.
As for sound, the pickups are pretty dark sounding (with a big low mid emphasis) while also being remarkably clear.
Geddy Lee's Power Windows tone is a good reference point, although he plays with a pretty aggressive attack.
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Mick Karn's fretless tone. Justin Chancellor is well known for playing a Wal, but (while very cool) I don't think of his tone as being all that representative of the Wal tone in general.
And I'm with you on preamps. All of my other basses are passive but the ACG/East preamp slices the sound in a vastly different (and to me awesome) way than a traditional 2, 3 or 4 band EQ.