The Collaborative International Dictionary of English v.0.48:

committed \committed\ adj.
   1. Bound or obligated, as under a pledge to a particular
      cause, action, or attitude. Opposite of uncommitted.

   Note: [Narrower terms: bound up, involved, wrapped up;
         dedicated, devoted; pledged, sworn]
         [WordNet 1.5]

   2. Associated in an exclusive sexual relationship; also
      called attached. Opposite of unattached.

   Note: [Narrower terms: affianced, bespoken, betrothed,
         engaged, pledged, promised(predicate); married]
         [Also See: loving.]

   Syn: attached.
        [WordNet 1.5]

   3. Consigned involuntarily to custody, as in a prison or
      mental institution.
      [WordNet 1.5]

The Collaborative International Dictionary of English v.0.48:

Engaged \En*gaged"\, a.
   1. Occupied; employed; busy.
      [1913 Webster]

   2. Pledged; promised; especially, having the affections
      pledged; promised in marriage; affianced; betrothed.
      [1913 Webster]

   3. Greatly interested; of awakened zeal; earnest.
      [1913 Webster]

   4. Involved; esp., involved in a hostile encounter; as, the
      engaged ships continued the fight.
      [1913 Webster]

   Engaged column. (Arch.) Same as Attached column. See
      under Attach, v. t.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Engage \En*gage"\, v. t. [imp. & p. p. Engaged; p. pr. & vb.
   n. Engaging.] [F. engager; pref. en- (L. in) + gage pledge,
   pawn. See Gage.]
   1. To put under pledge; to pledge; to place under obligations
      to do or forbear doing something, as by a pledge, oath, or
      promise; to bind by contract or promise. "I to thee
      engaged a prince's word." --Shak.
      [1913 Webster]

   2. To gain for service; to bring in as associate or aid; to
      enlist; as, to engage friends to aid in a cause; to engage
      men for service.
      [1913 Webster]

   3. To gain over; to win and attach; to attract and hold; to
      draw.
      [1913 Webster]

            Good nature engages everybody to him. --Addison.
      [1913 Webster]

   4. To employ the attention and efforts of; to occupy; to
      engross; to draw on.
      [1913 Webster]

            Thus shall mankind his guardian care engage. --Pope.
      [1913 Webster]

            Taking upon himself the difficult task of engaging
            him in conversation.                  --Hawthorne.
      [1913 Webster]

   5. To enter into contest with; to encounter; to bring to
      conflict.
      [1913 Webster]

            A favorable opportunity of engaging the enemy.
                                                  --Ludlow.
      [1913 Webster]

   6. (Mach.) To come into gear with; as, the teeth of one
      cogwheel engage those of another, or one part of a clutch
      engages the other part.
      [1913 Webster]

WordNet (r) 3.0 (2006):

engaged
    adj 1: having ones attention or mind or energy engaged; "she
           keeps herself fully occupied with volunteer activities";
           "deeply engaged in conversation" [syn: engaged,
           occupied]
    2: involved in military hostilities; "the desperately engaged
       ships continued the fight"
    3: reserved in advance [syn: booked, engaged, set-
       aside(p)]
    4: (of facilities such as telephones or lavatories) unavailable
       for use by anyone else or indicating unavailability;
       (`engaged' is a British term for a busy telephone line); "her
       line is busy"; "receptionists' telephones are always
       engaged"; "the lavatory is in use"; "kept getting a busy
       signal" [syn: busy, engaged, in use(p)]
    5: (used of toothed parts or gears) interlocked and interacting;
       "the gears are engaged"; "meshed gears"; "intermeshed twin
       rotors" [syn: engaged, meshed, intermeshed]
    6: having services contracted for; "the carpenter engaged (or
       employed) for the job is sick"
    7: built against or attached to a wall; "engaged columns"

Moby Thesaurus II by Grady Ward, 1.0:

93 Moby Thesaurus words for "engaged":
   absorbed, absorbed in, accessory, affianced, agreed, armed,
   arranged, arrayed, assured, at it, at work, battled, betrothed,
   bound, buried in, busy, caught up in, committed, compacted,
   compromised, contemplating, contemplative, contracted, covenanted,
   deep, deployed, devoted, devoted to, embattled, employed,
   engrossed, engrossed in, full of business, guaranteed, hard at it,
   hard at work, immersed, immersed in, implicated, in battle array,
   in harness, intended, intent, intent on, involved, lost in,
   meditating, meditative, monomaniacal, monopolized, obligated,
   obsessed, occupied, on duty, on the go, on the hop, on the job,
   on the jump, on the move, on the run, partaking, participant,
   participating, participative, participatory, pledged, plighted,
   preoccupied, promised, ranged, rapt, sealed, settled, sharing,
   signed, single-minded, stipulated, studious, studying,
   submerged in, swept up, sworn, taken up with, tied up,
   totally absorbed, undertaken, underwritten, warranted, working,
   wrapped, wrapped in, wrapped up, wrapped up in