稼ぐ：かせぐ：to earn money by doing xxx, to make a living at xxx. "She likes to DJ but she can't make a living at it."
暮らす：くらす：This doesn't correspond to any English word. Maybe the closest phrase is, "To lead one's life." Homeless people, retirees, rich divorcees all 暮らす even though they don't 稼ぐ。It means "to live in a place" as well as "to do all one's daily junk (eating, sleeping, hanging out)." 暮らす is usually used in sentances like, "over 30,000 people are living in the city." or "Live on $20 a day," or "Have an easy/hard life."
住む： すむ： this also means 'to live' but in the much more narrow sense of, 'to live at this particular address.' (i.e. I live with my parents / I live in an apartment / i live in this town)