I have had the same thing happen to a Singer 518. A squeek, just apears out of nowhere. Clean it till you can eat off the bed. Oil it, oil it, grease it, oil it till you think it would be better to just soak it in a tub of oil ... and it still squeaks.
Finally both my wife and myself said: "Run or blow up." She went on with her projects. Many hours later ( I could hear it squeaking all over the house she took a break. I pulled the top, oiled it again. Turned it over, oiled it again. Stood it on the hand wheel and oiled it some more.
She went back to sewing and it still squeaked.
Then I went downstairs and she was sewing away .... and ..... no squeak. My theory is that a piece of thread got stuck somewhere it wasn't supposed to be and had to work itself out.
I still hate that machine.
Joe