These are all adverbs used as the similar meaning as you can see. 지금(只今), now 바로, right/straight 당장(當場), at/on this very place 즉시(卽時), immediately 즉각(卽刻), instantly/promptly 곧, soon 냉큼, at once 지금 즉시 당장 곧바로 어서 빨리 오세요. Please come here fast immediately right now without delay

It is just my opinion. When I hear the words "당장,바로,즉시,즉각", it sounds "without delay" or "right now". And it is often used in a commanding or requesting tone. ex) 당장/바로/즉시/즉각 해라! (Do it right now!) However, "당장" sounds like the most strong expression. And "바로" seems a little more polite than the others. "즉시","즉각" seem to be formal compared to the others. These two words are used at the same time like "즉시즉각' (I've never heard "즉각즉시"). "곧" sounds to me like it meas the immediate future. ex) 우리는 곧 목적지에 도착할겁니다. (we are getting into the destination soon.)