Frank,

I suspect that most cheap fans have permanently lubed bearings. I doubt
that lubing the bearings will accomplish much. Won't hurt to try if you are
a DIY person. Light machine oil like 3 in 1.
Do others complain of the smell? Have you spoken to your physician about
your sensory and respiratory problems?
If you are using window box fans, turn them around so they are blowing
out rather than in.

Dave M.