This is a mid-1970's Schwinn. Obviously, if there is grit or dirt or rust I will clean them. My instinct is to use 3 in 1 oil if I must, then repack everything in good old reliable bicycle grease. But if there is just old grease without anything gritty, do I even need to clean the bearings etc., and if so, what cleaning agent do I use?
brake cleen works the best. teflon bike grease is best but automotive wheel bearing grease works good too. i would just replace ball bearings regardless of how old they may be. yes clean out old grease.
any other like item such as Park polylube 1000 is fine too. Dont use 3 in 1 oil it is too viscous and will break down as a lube in bearings .
Generally speaking, when I am re packing a hub, if it was really dirty, I replace the ball bearings, I buy them by the hundred at very little cost. That way I avoid putting worn bearings back in the hub. If I don't have replacement bearings, I keep the bearings from each side of the hub separate, and put them back on the side they came from, in case the bearings from one side of the hub are more worn than the ones from the other side.
To clean bearings of grease you want to use a solvent. Several are available. Find one of these; mineral spirits, kerosene, or brake wash (aerosol). Use a parts cleaning brush and don't drop a bearing. Once they hit the floor they run and hide. Hard little critters to find, too. I use a magnet to pull the bearings out unless the old grease is too thick. The balls themselves can be put in a jar or tin with the solvent and soaked. Clean the race with the brush. I use an old metal coffee can to place the hub over and dip the brush in the can. It runs back inside to contain the mess. If you have compressed air you can blow them dry. If not you can force a piece of clean rag through the hub to dry. Inspect the clean race for pitting. (If there is pitting the race needs replaced and in most instances that will require a new hub.) Press the new grease in the race with your finger and place the balls one by one into the grease pressing them in. The new grease will hold the bearings from falling out. Don't worry if you think you are using too much grease, the excess will ooze out as you install the axle and you can wipe it off. Don't over tighten the axle nuts. There is a fine touch between play and over tight. With new grease I tighten them them to space the balls properly, then back off and tighten them for the proper feel.
Never use 3 in 1 oil for anything on a bike. Ever. You should clean everything, don't just relube since there are some greases and oils that aren't compatible. I use degreaser like Fast Orange or Simple Green (kerosene, gasoline, and other things are way too flammable), or if it's really bad I use WD40. The bearings are probably in retainers. Pop the bearings out and clean inside the retainers too. If there is a bearing supply place near you take one of each size and get new bearings... a box of 100 costs VERY little. Once clean, repack with white lithium greae... a tub of this stuff costs almost nothing and will last forever. Don't pile in the grease. Just lightly coat the races and roll the bearings around on a greasy finger then reinstall. Putting in too much grease just attracts dirst and INCREASES friction. Good luck!