Why is the water 'running' throughout the night? Is the sprinkler system on? Do you have a leaking toilet? What are you running/flushing when you hear the whining? Do you have well water? Do you know the pressure going INTO the house?
My first guess is that the refill valve in the toilet is the problem. The washer and/or gasket in it may need replacement. (As an aside, maybe someone can tell me if you can replace just the washer and/or gasket in the refill valve, and how to 'remove' the 'cap' on the top w/o damaging the entire float system.) Anyways, the whining sound occurs when the toilet is refilling.
If the cause of your problem is different, let 'us' know.