My physics teacher (years and years ago) used to say "erg equals work". I have never forgotten that!
In ancient Greek--since it was a slave culture--there was a huge difference: the identical word εργασία meant work-labor-occupation, whereas δουλεία referred to slavery. Words for work-labor (ἔργον, ἐργατεία) were associated with the verb ἐργάζομαι, while slave labor of a δοῦλος, η was related to the verb δουλεύω. Although slavery is no longer legal in most parts of the globe, with human trafficking there are more slaves--forced labor--globally than ever in human history (in sheer numbers). We'll have to hear from a Greek speaker to find out if this background is useful for understanding modern Gk ways of referring to people who are enslaved (forced labor). My old Mandeson dictionary says that one word for "enslavement" in modern Gk is η δούλωσις, whereas η εργασία refers to work-labor-business-job.
Εργασία has the same meaning as δουλειά but it is a bit more formal. Δουλεία still means slavery. Pay attention to the accents. Δουλειά is work (λεια is one syllable), δουλεία is slavery.