Nicole,
You sound like you are having fun with this new house! Have you tried placing your hand on the wall behind the washer as it cycles. You will probably feel a pipe slamming in a stud or header as the water shuts off.
If it is pipe hammering then you will need to install either an expansion tank (arrester) or a pipe riser to cushion the hammering.
A short term solution would aslo be the close down the valves feeding the washer so that it takes longer to fill but reduces the chance of pipe hammer.
Good luck, Jim
'Just a handyman trying to help'