Strats are generally noisy because they generally have single coil pickups which pick up all the radio interference noises given off by computers, screens, amplifiers, light dimmers and anything else. The hotter the pickup output the worse the noise problem. Telecasters are generally noisier than Strats and P90 pickups noisier still.
Technological solutions are to change the pickups for Lace sensors (still single coil but much less hum, though some think they sound "sterile", I happen to like them). Or replace the pickups with "noiseless" ones. These are really variations, depending on make and model, of dual-coil humbuckers. They do alter the tone (often quite a lot) and sometimes the volume and tone pots have to be changed as well. It can be worth while thoroughly shielding the pickguard and control cavity as well, though Fender seem to do a reasonable job of it mostly. Switch positions two and four are usually humbucking on modern Strats because the middle pickup has reverse wiring and magnets to the other two and the combinations make a humbucker.
However, if you want the classic single-coil Strat sound you need single coil pickups. You can use noise gates but they have consequences for attack and sustain.
Guitar forums are full of discussion about this, and google can be very useful as well.
What kind of noise are you getting? Hum/buzz, whining, chattering noises? The simplest solution if practical is often to find a spot where the noise is least obtrusive and play there.