Speaking of new valve stems, I've also had a third party replacement valve stem cause this problem. In my experience substitute faucet parts often don't work properly. Try to get replacement parts made by the manufacturer of your faucet. If you can't find the parts locally, they all have customer service 800 numbers. High water pressure can cause a variety of odd problems including these noises.
High pressure can also damage toilet valves and other devices connected to the plumbing.
If you're on a city water system, ask your neighbors if they are having similar problems. If you have a well you probably have a water pressure meter. If you don't have one, borrow one or, buy one at the hardware store and check the pressure. 60psi you may want to adjust your pressure reducer or install one. Sometimes these sounds are caused by the pipes rubbing or bumping inside the walls because they aren't strapped down well or, because their stud pass-through holes are too small or off center.