I don't want to sound like a wise ass here, but bikes are so cheap you could get another for about $100 if the noise bothers you that much. Or you could just buy a good set of rear sprockets and derailers. It sounds like the ones you have are (pardon me for assuming) kinda low end/ low quality.
Look at it this way, if you put the cash into some better parts, you can enjoy the bike until *another* component fails.
