The Collaborative International Dictionary of English v.0.48:

Exude \Ex*ude"\, v. t. [imp. & p. p. Exuded; p. pr. & vb. n.
   exuding.] [L. exudare, exsudare, exudatum, exsudatum, to
   sweat out; ex out + sudare to sweat: cf. F. exuder, exsuder.
   See Sweat.]
   To discharge through pores or incisions, as moisture or other
   liquid matter; to give out.
   [1913 Webster]

         Our forests exude turpentine in . . . abundance. --Dr.
                                                  T. Dwight.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Exude \Ex*ude"\, v. i.
   To flow from a body through the pores, or by a natural
   discharge, as juice.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "exude":
   bleed, discharge, drip, effuse, egest, eliminate, emanate, emit,
   excrete, exfiltrate, extravasate, exudate, filter, filtrate,
   give off, leach, lixiviate, ooze, pass, percolate, perspire, reek,
   secrete, seep, sew, strain, sweat, swelter, transpire, transude,
   trickle, weep, wilt