1. 'Right away' is like 'straight away' - it means immediately or without delay.
For example: 'This job is urgent, so you should do it right away.'
2. 'Right now' is simply an emphasised version of 'now'. For example, 'Right now, I'm feeling really confused.'
You can emphasise many words by adding 'right', for example, 'Right here' or 'Right next to me'.