Discussion Forum—A Way with Words, a fun radio show and podcast about language

The phrases "right away" and "right off" both mean "without delay". And the word "right" is just to emphasize the word after it. The problem is "away" and "off". If we see "away" and "off" in a literally way, there's nothing to do with "without delay or immediately". Does anyone know why the two phrase collocate in this way? What are the origins of them? Thanks!