They are all very similar. I use 'right now' when I want to know what you are doing this exact second, while I use 'now' for this moment generally. I use 'right away' when I am responding to a request to do something. Q: "What are you doing right now? Can you please close the window?" A:"I'll do it right away now that I have finished reading"

Also, all 3 of them are appropriate to use in reference to oneself, (such as I will do that now/right now, right away.)

What a great question! "Now" and "Right now" are generally interchangeable... "Right now" will often be used for emphasis that it is to occur immediately, it will usually be used by a superior to a person of lower position, such as a parent ordering a lazy child to take out the trash ("Young man, you take that trash out right now!"). To say that something must be done "Right away" is a subtle shift from "right now" or "now." Typically "right away" means "now, if at all possible, but a very short delay is probably ok if you are doing something of very high priority at that very moment. Julia

great question