The Collaborative International Dictionary of English v.0.48:

Illogical \Il*log"ic*al\, a.
   Ignorant or negligent of the rules of logic or correct
   reasoning; as, an illogical disputant; contrary of the rules
   of logic or sound reasoning; as, an illogical inference. --
   Il*log"ic*al*ly, adv. -- Il*log"ic*al*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

illogical
    adj 1: lacking in correct logical relation [syn: illogical,
           unlogical] [ant: logical]
    2: lacking orderly continuity; "a confused set of instructions";
       "a confused dream about the end of the world"; "disconnected
       fragments of a story"; "scattered thoughts" [syn: confused,
       disconnected, disjointed, disordered, garbled,
       illogical, scattered, unconnected]

Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "illogical":
   aberrant, abroad, absonant, adrift, all abroad, all off, all wrong,
   amiss, askew, astray, at fault, awry, beside the mark,
   contradictory, contrary to reason, corrupt, deceptive, defective,
   delusive, deviant, deviational, deviative, distorted, errant,
   erring, erroneous, fallacious, false, faultful, faulty, flawed,
   heretical, heterodox, illusory, inauthentic, inconclusive,
   incongruous, inconsequent, inconsequential, inconsistent, invalid,
   irrational, loose, nonscientific, not following, not right,
   not true, off, off the track, out, paralogical, peccant, perverse,
   perverted, reasonless, self-annulling, self-contradictory,
   self-refuting, senseless, straying, unauthentic, unconnected,
   unfactual, unorthodox, unphilosophical, unproved, unreasonable,
   unscientific, untrue, wide, without reason, wrong