I'm having trouble understanding what social oppression is. Can it be applied to poor hating on other poors?

Social oppression:

"The systematic, socially supported mistreatment and exploitation of a group or category of people by another."

http://www.webref.org/sociology/s/social_oppression.htm

Yes, social oppression has often been imposed by poor whites on poor blacks.

Years ago when I lived in an all-white, low-rent apartment complex, my neighbor's disdain for blacks was strong. I felt that my neighbors had to feel superior to someone -- and the blacks were lower in the social hierarchy.