Toilets can make noise for many reasons: the most common are bad fill valves, calcium deposits inside pipes and leaky toilet valves. In most cases, a cleaning or replacement is needed to correct the problem.
Vibrating sounds heard in the wall when a toilet is flushed are usually caused by the fill valve. Inside a fill value is a diaphragm gasket, and when it goes bad the gasket loses elasticity and gradually hardens. To test for a bad fill valve, remove the tank lid and gently lift on the fill valve's float arm. If this causes the noise to stop, the fill valve will need to be replaced.
A whooshing sound heard when a toilet is filling that goes away after the toilet is full often occurs when the water pipes are starting to develop build-up inside. This happens most often with galvanized and copper pipe because the turns are harder and reverberation occurs because the pipe is made of metal. The pipes need to be cleaned with an appropriate cleaning agent for calcium and mineral deposits.
Slowly leaking toilet fill valves can cause a whistling sound from a toilet. Adjust the fill valve until the whistling stops. The leaking valve will likely need to be replaced or repaired.