Ok, virbration at the body end... try detuning then pulling the bridge pins - refit, but hold the string back against the body when pushing in the pins. this will ensure the ball end of the string will be snug against the body and not vibrating around.
On second listen to the soundbite you recorded it seems that you might be playing a harmonic instead of muting - try muting until the string isn't moving anymore, and dont mute on the 12th,7th or 5th fret.
I'll give this a go when I get home tonight.
As for the soundbite, All i did was pluck the high E open, put my finger on it by the sound hole to mute it, and plucked again and so on. Everytime I muted it, the E string did stop vibrating but the humm persisted from the A and D string.
From what I've read it's normal to have some sympathetic vibration but on mine it seems unbearable, to the point where It doesn't sound right. And I'm a beginner, started a week ago, so still figuring out what's normal and whats not.