Adrian Belew has some incredible sounds coming out of his Strat - one of them is the quasi-Elephant sound on Elephant Talk - King Crimson - "Discipline". I've watched him do it live but apart from the actual neck bending and whammy bar machinations I've still not been able to duplicate it...Help!!
You can also get a similar sound as follows:
Bend both notes up half a tone to a tone at the end; and if you have a tremolo; give it a pull or push; Adrian Belew seems to do both at different times in that track. His tone also seems very reverb heavy so stick some on there for a closer sound.
Also move the notes around for different pitches of elephants
Which i think is more accurate in the case of Elephant talk
Adrian Belew released a VHS in the 80s called Electronic Guitar. Elephant Talk is one of the songs he talks about.
He clearly explains how he achieved the Elephant-like sound. But the only thing I can remember is that he used a flanger.
I have the tape somewhere at my parents'. I'll have a look at it next time I visit them (in about two weeks actually) and I will edit this answer.
You can also find used copies at Amazon.
EDIT: My VCR is broken. Sorry but I can't help more.
Edit: [Direct reference to this Technique on YouTube]
Sounds to me as though he's doing the same thing Hendrix did on "Highway Child", which is to play a note on the B-string while simultaneously bending the note two frets higher on the G-string almost a whole step. This makes the two notes almost, but not exactly, the same pitch, which, when combined with distortion, gives that growly sound. Now whammy that up, and you've got yourself an elephant.
Also, the trick with the flanger effect is to use something that's definitely NOT subtle. In fact, you'll want to use such a heavy flange that it begins to sound like a chorus, noticeably warbling the pitch back and forth and not just the phase. MAX pitch and/or speed controls on your flange at home should get the near vibrato effect it actually creates.
(Even the vibrato function on a UniVibe or reproduction will get very close to this too).