Sounds like you may just have a faulty water inlet valve in a toilet tank. Turn the water off to each toilet one by one to find it, and then replace the valve with a Fluidmaster 400A float-cup type. They are very inexpensive and have easy illustrated installation directions.
Something else to check is wheter or not you have a vacuum breaker attached to the hosebibb (the faucet). This will be a brass fitting that is screwed onto the hosebibb where the hose attaches. It is designed to prevent water from flowing back into your house system in the event of a problem. Sometimes a bad vacuum breaker will cause a loud whine or hum hroughout the water system when something is running.
If your hosebibbs have the vacuum breakers attached, temporarily removing them will let you find out if this is the problem. If so, just get some new ones and screw them on. The old ones may have a set screw in them which will need to be drilled out in order to remove them. This is fairly simple to do, just don't drill too deep.