Check the hubs by trying to move the rim side to side in the bike frame to see if there is play. Also good to pull the wheels off and turn the hub bearings by hand to see how they feel, either smooth or tight or with crunchy spots. While you have the rear wheel off, spin the cassette or freewheel to see that it works properly.
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