I presume you have other guitars that don't buzz anything like this when used in the same location with the same amp (+any effects)?
Did you run a ground wire to the bridge post and solder it to the back of a pot? If not, you need to do so. If you did, then you need to check with a multimeter that it's still making a connection. If not then it needs to be redone as the wire could have broken or pulled loose.
If you haven't got a digital multimeter, now is the time to get one. They don't cost much - $30 should get you a decent one and they are so useful in checking out any wiring issues.
You probably ran a separate ground lead to the 3-way selector switch. So touching the switch connects your body to ground, both making it a big earth plane and absorbing a lot of RFI, and also channelling any electrical noise your body may be making down to ground. The same would happen if the strings are grounded correctly.
With both tones turned down fully, there is a very good path to ground through the tone capacitors for all but the lowest frequencies. This is RFI noise you're hearing, not mains hum, so most of the interference being picked up is higher frequency noise, which is why it disappears when you turn the tone pots down.
Thanks for all the great advice. As it turns out, after taking a closer look I created a ground loop with my original wiring. So I fixed the problem now the buzz is barely noticeable . I can live with it.