Oil on stator windings, commutator, and armiture
Your circular saw most likely has a AC/DC universal motor. This one has a commutator and contact surfaces. Avoid putting oil on the contact surfaces, it will burn from the bit of arcing which is unavoidable. Such surfaces are lubed with graphite, not oil.

A refridgerator compressor motor however is always a shaded pole asynchronous AC motor. It doesn't have any contact surfaces. So it's safe to lube it with oil.