These three words means "work." Trabajo is effort, sweat. Labor is craftmanship, work as value. Obra is the work as product, oeuvre. When you think about your "work," what are you really thinking about? For me it's mostly the second term, labor. The obra is just evidence of previous labor. With trabajo there is too much evidence on the sheer effort involved. Ay qué trabajo me cuesta / quererte como te quiero.
If they furlough us, as they keep threatening to do, they cannot effect labor or obra, only trabajo.