Aside from oiling, have you lubed the gears? Lube *goes* get old, sticky and gummy. On old machines I get a tube of sewing machine lubrication, try to scrape off as much as I can of the old stuff on the gears, then add new lubrication. Just be careful where you put the lubrication -- it goes *only* on gears (the things with teeth).
It may be that when you put new oil on, there's enough excess oil to compensate for sticky gears.