Always oil in a sleeve bearing, and grease in a ball bearing. If it is preventative, use a very light oil. If it has already worn the bearing and is making noise, use a thicker oil. It will not be drawn through the bearing well and need reapplied more often but once you have the wear you need a thicker film to (try to) keep the wobbling to a minimum.
I've had great success relubing sleeve bearings in everything from HVAC to computer fans, box fans, appliance motors, etc. I've had no problem using detergent oil, even a decade later in some cases but IMO that's around the outer limits of how long it'll be till it needs relubed again unless there is a substantial oil reservoir you fill. w/o a reservoir it's usually more like every 3 years depending on running hours and amount of wear already present.