Ethel,
I have a Pfaff that gave me fits. The needle would not move right on zz. I oiled and oiled that machine. ANYTHING that remotely moved got oil. I oiled and turned it on its side, I oiled and turned it on it's other side. I turned it upside down. I stood it on end. That thing spent the winter under my bench in one position or another. I tested Kroil on that machine and it would not budge side to side very fast. One day a chunk of broken needle fell out of somewhere as it was turning. It must have been jammed in there somewhere.

Usually when a machine won't zig there is a broken or cracked gear or cam stack. Get a decent light and look at all gears and cam stack to check for cracks and breaks.
Some times there is an adjustment that needs to be made.
Neither a do it yourself project with out a service manual.