What would make...

Sounds like that to which you connect the guitar to needs a ground.

That's because when you touch the jack, the noise vanishes. The jack you touch is where the cable plugs-in, isn't it?

So that cable goes to an amp or preamp, and I would test if that is grounded, which should ground its jack. If not grounded, then test by grounding it in a preliminary way to see it that solves the problem.

Just a guess, though.

Connecting a wire to the body cavity only works if the body cavity is lined with shielding material.

As suggested above, if you need to touch your strings to reduce the hum, you probably need to attach a ground connector to your bridge which will be connected to your strings etc.

Didn't your tech tell you that before selling you new pickups?

best regards,
mike

Go over to your buddies place or another music shop. Plug into thier amps and see if it is still making that noise.

Does it have a whammy bar?

Strats are sort of famous for that connection breaking loose after to many bends on the whammy bar... but it's always simple to reconnect.

best,
mike

Thanks for the replies everyone.  Lotta good stuff there.  Before I took it in it hummed no matter which posistion the switch was in as long as I wasn't touching the strings.  My tech made it to where it only hummed when the switch is set to use, solely, the neck pick-up, and thats only if I have distortion or any gain at all.  It doesn't hum at all on any sort of "clean" effect.  I opened it back up and replaced the ground that goes to the bridge and springs with a solid #12 aluminum wire and that has reduced it a little but it's still not as quiet as I'd like it to be.  As far as a sheilded lining, the underside of my pick guard has this lining but the body cavity does not.  Installing that will be my next move.  While I had it back open I checked all the wiring against the diagram I have and everything looked kosher.  My music room is small and crammed full of electronic devices but none of it seems to effect my other guitars.  I did get out the ol' ohm meter and there is in fact continuity between all the pots and the ground so,  I don't know.....those new pick-ups sound mighty good with just some reverb and a little chorus.  As long as theres no distortion or gain it's quiet as a church mouse. 

I FIXED IT!!!
I took everything back apart and lined the body cavity with some of that silver metal tape (I call it thousand mile an hour tape) and made sure it was bonded to the lining under my pick guard and all the pots and bridge.  Now it doesn't make a sound.  It's like I have a brand new guitar.  Thank you everyone for your replies.