The Collaborative International Dictionary of English v.0.48:

Right \Right\, adv.
   1. In a right manner.
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   2. In a right or straight line; directly; hence; straightway;
      immediately; next; as, he stood right before me; it went
      right to the mark; he came right out; he followed right
      after the guide.
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            Unto Dian's temple goeth she right.   --Chaucer.
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            Let thine eyes look right on.         --Prov. iv.
                                                  25.
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            Right across its track there lay,
            Down in the water, a long reef of gold. --Tennyson.
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   3. Exactly; just. [Obs. or Colloq.]
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            Came he right now to sing a raven's note? --Shak.
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   4. According to the law or will of God; conforming to the
      standard of truth and justice; righteously; as, to live
      right; to judge right.
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   5. According to any rule of art; correctly.
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            You with strict discipline instructed right.
                                                  --Roscommon.
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   6. According to fact or truth; actually; truly; really;
      correctly; exactly; as, to tell a story right. "Right at
      mine own cost." --Chaucer.
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            Right as it were a steed of Lumbardye. --Chaucer.
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            His wounds so smarted that he slept right naught.
                                                  --Fairfax.
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   7. In a great degree; very; wholly; unqualifiedly; extremely;
      highly; as, right humble; right noble; right valiant. "He
      was not right fat". --Chaucer.
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            For which I should be right sorry.    --Tyndale.
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            [I] return those duties back as are right fit.
                                                  --Shak.
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   Note: In this sense now chiefly prefixed to titles; as, right
         honorable; right reverend.
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   Right honorable, a title given in England to peers and
      peeresses, to the eldest sons and all daughters of such
      peers as have rank above viscounts, and to all privy
      councilors; also, to certain civic officers, as the lord
      mayor of London, of York, and of Dublin.
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   Note: Right is used in composition with other adverbs, as
         upright, downright, forthright, etc.
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   Right along, without cessation; continuously; as, to work
      right along for several hours. [Colloq. U.S.]

   Right away, or Right off, at once; straightway; without
      delay. [Colloq. U.S.] "We will . . . shut ourselves up in
      the office and do the work right off." --D. Webster.
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WordNet (r) 3.0 (2006):

right away
    adv 1: without delay or hesitation; with no time intervening;
           "he answered immediately"; "found an answer
           straightaway"; "an official accused of dishonesty should
           be suspended forthwith"; "Come here now!" [syn:
           immediately, instantly, straightaway, straight
           off, directly, now, right away, at once,
           forthwith, like a shot]
    2: at once (usually modifies an undesirable occurrence); "he
       promptly forgot the address" [syn: promptly, right away]

Moby Thesaurus II by Grady Ward, 1.0:

46 Moby Thesaurus words for "right away":
   PDQ, all at once, all together, apace, at a blow, at a stroke,
   at once, at one blow, at one jump, at one stroke, at one swoop,
   at one time, decisively, directly, expeditiously, forthwith,
   immediately, in a hurry, in no time, instanter, instantly, now,
   on the instant, on the spot, per saltum, pretty damned quick,
   promptly, pronto, quickly, right now, right off, simultaneously,
   smartly, speedily, straightaway, straightway, subito, summarily,
   swiftly, then and there, this minute, this very minute, uno saltu,
   with all speed, without delay, without further delay