Besides oiling everything that looks like it should move, take the top off and look down behind the knobs on the inside.
Kenmores have very complex controls and without a manual it's often difficult to get them to work correctly.
Make sure when the stitch length knob is turned, it does move the linkage inside the machine. We had a Kenmore here not long ago that had a roll pin missing in the stitch control assembly.
I have machines that are close to yours model number wise, but I can't say for sure how yours works. Even one model apart will have differences to the controls.
A manual is mandatory for these Kenmores in my opinion. Sears "should" have one for your model.
Joe