The headset could be too tight or too loose or have worn bearings. What type of headset do you have? Assuming you have a threadless headset, changing the stem requires loosening and retightening the headset. The top cap allen fitting is used to adjust the headset tension while the stem attachment to the fork is loose. Tighten enough to remove all the play but not to cause binding. Then tighten the stem onto the steerer tube of the fork. See the parktool website for specific directions.
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