I have a 1997 Honda Odyssey EX since 1997.
One of the Rear Auto Door Locks often makes clicking noise. But since last week, it makes loud "Z" noise.
Also at 90,000 miles a balancer seal blew off and ruined timing belt and all other belts with engine oil.
Something tells me that replacing the timing belt would have fixed this problem before it happened; or maybe driving it crazy made it happen. In the world of engines, things also can just wear out, on any car, no matter what make it is.
The "Zzz" whine sound from your door lock is most likely the electric door lock actuator. There is a pinion gear that drives a rack gear back and forth to move the lock up and down, depending upon the polarity of the voltage applied to the actuator. At each end of the rack gear there is a little rubber bumper stop. If that rubber bumper stop wears out or gets displaced, the rack gear will move beyond its limit, and the pinion will spin past the end of the rack. The Zzzz sound you hear is the pinion gear grinding away at the teeth off the end of the rack gear.
You have two solutions:
(1) Replace the door lock actuator. You can buy a genuine Honda replacement part for about $113 (if you shop around) and install it yourself, but it's sort of a pain to do, and it takes quite a bit of patience to remove the door panel, handles, latch, etc. You might just want to have a dealer do it for you.
(2) If you are a hard-core do-it-yourselfer, you can remove the failing actuator, open that little guy up, and using some RTV silicone, you can "cast" or "mold" a replacement rubber bumper stop to keep that rack gear within limits. (Make sure you let the silicone set up for several hours, so that it's good and hard before you test the actuator.) This is actually a very good solution that can be accomplished for a $5 tube of silicone and an afternoon of patient putzing.
Good luck!