In general, now refers to this very moment. Currently is a slightly more general word to describe the timeframe we are in. For example, "I am at your house now" versus "Currently I am learning English".

'Currently' implies that the situation may change, whereas 'now' does not. 'Currently' is similar to 'at the moment', in this respect. 'I'm working at Head Office now'. This suggests that you expect to remain working at Head Office. 'I'm currently working at Head Office.' 'I'm working at Head Office at the moment.' This suggests that the situation is temporary and that you expect to be moved to another location at some point.