When I play my strat alone (not plugged into the amp) there appears to be a resonating sound coming from the strings. It's not to do with my noise control because open strings sound a lot different and I have that under control! I have a Floyd Rose trem on the strat if that has anything to do with it? Also, I had a new scratch plate fitted a while back and the guitar service guy had to drill a few extra holes in the guitar so it would fit, would that be the problem? The strat is fine when it's plugged into the amp, just curious what's causing the ringing when I play acoustically...
If you can't hear it when amplified, I wouldn't worry about it. You'll quite frequently hear odd noises when playing without an amp, but not hear them when plugged in. It's when you hear them through your amp that you need to fix something.
your ringing is most likely the springs in the back of the guitar holding the floyd. my strat has the stock bridge and when i play hard i hear them resonating in the back. especially if i slam on a note then mute it right away (sort of a funk style hit).
Springs from your trem, you could try and wind a bit of cloth around them (not too tight!) to mute the ringing.
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It's your strings, they vibrate and make sounds.
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Quote by Gundamnitpete
It's your strings, they vibrate and make sounds.

Nice shot at being sarcastic there.

TS, as has been said before, these are your tremolo springs. They're under such tension constantly, they're basically strings themselves, rattling around in the magnetic field of your pickups. Take off the backplate, get some cotton wool or tissue paper in there or under the springs and fit the backplate back on. That will solve all your problems.
Note that the vibrating springs are probably a good portion of your sound, make sure to check if it changes with the cotton wool, and whether or not you like the change!