Best case replace the headset bearing.
Or remove them, give them a good soaking...WD40 works adequately...then a good scrub with a tooth brush...thoroughly scrub the inside of the headset with brush and WD...wipe everything clean and dry...perhaps spray again and clean/dry again to remove anything lingering/hiding...apply grease to headset races...apply grease to bearings in their cages...reinstall and adjust. Unless the bearings have rust on them, are pitted, are deformed, etc. they might be fine. Always inspect the bearings, cages and headset races for wear and damage...ie...dings on the race, brinneling sp?, that could cause a steering problem...'self aligning steering' lol.
I prefer never to use cages, rather loose bearings which allows for one additional bearing...might be a bit more work to service but better imo.
Headsets are inexpensive...it is better to replace old and not well serviced but at least servicing old ones is better than nothing.
Good luck and keep us informed...