What is going on here is pretty simple. You must be close to an AM or
FM transmitter. Either a semiconductor part or corroded connection is
acting as a rectifier -- "crystal set," if you like. See if there are
any clearly corroded connections in the system, especially if you live
by any body of water. Here at the Delaware shore I've used a lot of
silicon grease on stuff for just that reason. Also see if one
telephone is more of a problem than another.

/paul
W3FIS