YOu may know already, but the screw in front of the pillar by the belt secures the front of the head to the case. Once you unscrew it you should be able to rock the head back on the hinges for routine service. However, in you case you'll need to undo the set screws at those hinges to be able to take the head out for a full oiling. oil everything that moves..or should. You shouldn't need to disassemble it much at all. Using water over the decals can turn the gold to sliver. I won't get near water with my machines. There are folks who swear by specialty lubes, but I generally use sewing machine oil for everything on a treadle. Some motors take grease.
I wouldn't use wood oil on metal.
Be gentle with it.. patience is a huge key on these. oil it and wiggle every day may be necessary. hair dryer heat can also loosen up dried oils.