Synonyms for Right away:

adv

punctually (adverb)
precisely, punctually, at once, immediately, speedily, sharply, forthwith, promptly, quickly, expeditiously, straight away, swiftly, instantly.

adv.

all (adverb)
promptly.
at once (adverb)
straightaway, immediately.
punctually (adverb)
precisely, punctually, at once, immediately, speedily, sharply, forthwith, promptly, quickly, expeditiously, straight away, swiftly, instantly.

n.

right away (noun)
forthwith, immediately, directly, instantly, now, at once, promptly, straight off, straightaway, in real time.
without delay (noun)
first off, instant, time.

Other synonyms:

without delay
instant.
Other relevant words:
in real time, first off, straightaway, now, directly, straight off, at once, instant.