The Collaborative International Dictionary of English v.0.48:

Strenuous \Stren"u*ous\, a. [L. strenuus; cf. Gr. ? strong,
   hard, rough, harsh.]
   Eagerly pressing or urgent; zealous; ardent; earnest; bold;
   valiant; intrepid; as, a strenuous advocate for national
   rights; a strenuous reformer; a strenuous defender of his
   country.
   [1913 Webster]

         And spirit-stirring wine, that strenuous makes.
                                                  --Chapman.
   [1913 Webster]

         Strenuous, continuous labor is pain.     --I. Taylor.
   [1913 Webster] -- Stren"u*ous*ly, adv. --
   Stren"u*ous*ness, n.
   [1913 Webster]

WordNet (r) 3.0 (2006):

strenuously
    adv 1: in a strenuous manner; strongly or vigorously; "he
           objected strenuously to the stand his party was taking"

Moby Thesaurus II by Grady Ward, 1.0:

47 Moby Thesaurus words for "strenuously":
   actively, animatedly, ardently, arduously, assiduously,
   bec et ongles, briskly, con brio, difficultly, diligently,
   effortfully, energetically, fervently, forcefully, forcibly,
   hammer and tongs, hard, hardly, heart and soul, heartily,
   indefatigably, industriously, intensely, keenly, laboriously,
   lustily, manfully, operosely, painfully, relentlessly, sedulously,
   spiritedly, the hard way, tirelessly, toilsomely, tooth and nail,
   unsparingly, vehemently, vigorously, vivaciously, with a will,
   with difficulty, with effort, with much ado, with pep, zealously,
   zestfully