Can I use a company logo in a painting that I'm going to sell? How?

That can be tricky and the answer will depend on a bunch of details that you have not included. Plus you will want to explore variations that are safer and less safe. You should talk privately with an intellectual property attorney so that you can safely discuss your plans in confidence and explore the options you have.

This is a complex issue. Andy Warhol made a fortune painting Campbell Soup cans and Campbell's didn't complain because it was great free publicity. Warhol didn't do anything to diminish the value of the company's product or logo. However, most companies probably aren't going to be so forgiving. Also, you'll have to be careful that you don't use the mark in any manner that might give consumers the idea that your painting comes from or is approved by the owner of the mark. I.E. you can't include the mark in order to increase the chances of selling the painting. Especially if the mark is owned by the Disney company or a sports franchise.

NO. The use of a company logo without permission from the owner would likely violate both trademark law and copyright law. Create a totally new version - think of an abstract version of the Fenway Citgo sign - colors and basic shapes might be okay to copy - but the art should be your own.