Ethel.
From the pictures it does not look to me like the needle bar is the only place that machine is bound with rust. Like Joe said float every thing in oil. That means everything in the front, top and bottom not just the needle bar. The hot sun will help thin the oil. My self I use Zippo Lighter Fluid (Benzene) to thin the oil to make it flow into the tight spots. That idea is frowned upon by many on this blog however. It works for me and I never have had a paint issue with it. I still try to keep any solvent off of the paint.