Q: "I have two different reels that worked fine for some time, but now, when a fish takes off, both have a shrill, whiny noise, and the drags tend to chatter slightly. How might I get rid of this noise?"
A: The best answer is to send the reels back to the manufacturer. Most companies have developed a special grease that works well with their reels.
However, for several years, I have had great success using Cal’s 2-Speed grease on my fly, plug and spinning reels. You can find it through Google, and it’s inexpensive. Carefully clean the washers with alcohol to remove the old grease. Allow 24 hours for the washers to thoroughly dry. Spread a thin layer of grease evenly on the washers with your fingertip. Remove all but a thin film. Reassemble, and your reels should be fine.