The hub cones are loose. Remove the wheel from the bike, grab the axle and move it side to side, back and forth. You'll feel the axle moving relative to the wheel. The cones need to be adjusted. Should only take 10 minutes to make the adjustment if you have the tools and know how to do it. But overhauling the hub with new bearings and grease might be recommended as well. Drop the wheel at your LBS to get this done right away. You damage the hub by riding it like this.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72