Mellotronists

The "odd oscillating synth sounds" in Wild Honey were created with an
electro-theremin known as the tannerin.

It's a sine-wave oscillator with the frequency controlled by a
mechanical slider (ribbon controller). 

There's lots of info about it here:
http://www.tompolk.com/Tannerin/Tannerin.html

I remember "inventing" one as a kid using a Knight Kit and some
resistive wire but I disliked the oscillator sounds and didn't believe
they should be used in music.