The Collaborative International Dictionary of English v.0.48:

Expeditious \Ex`pe*di"tious\, a.
   Possessed of, or characterized by, expedition, or efficiency
   and rapidity in action; performed with, or acting with,
   expedition; quick; having celerity; speedily; as, an
   expeditious march or messenger. -- Ex`pe*di"tious*ly, adv.
   -- Ex`pe*di"tious*ness, n.

   Syn: Prompt; ready; speedy; alert. See Prompt.
        [1913 Webster]

WordNet (r) 3.0 (2006):

expeditiously
    adv 1: with efficiency; in an efficient manner; "he functions
           efficiently" [syn: efficiently, expeditiously] [ant:
           inefficiently]

Moby Thesaurus II by Grady Ward, 1.0:

81 Moby Thesaurus words for "expeditiously":
   PDQ, agilely, amain, apace, at flank speed, at once,
   by forced marches, cursorily, decisively, directly, double-quick,
   effectively, fast, feverishly, flat-out, forthwith, furiously,
   hand over fist, hand over hand, hastily, hell for leather,
   hell-bent, hell-bent for election, helter-skelter, hotfoot,
   hurriedly, hurry-scurry, immediately, in double time,
   in double-quick time, in high, in high gear, in no time,
   in passing, in seven-league boots, instanter, instantly,
   lickety-cut, lickety-split, nimbly, on the double, on the instant,
   on the run, on the spot, pell-mell, post, posthaste,
   pretty damned quick, promptly, pronto, punctually, quick, quickly,
   rapidly, readily, right away, right off, slapdash, smartly,
   snappily, speedily, spryly, straightaway, straightway, subito,
   summarily, superficially, swiftly, trippingly, under forced draft,
   whip and spur, with a rush, with all haste, with all speed,
   with dispatch, with giant strides, with haste, with rapid strides,
   with speed, without delay, without further delay