The Collaborative International Dictionary of English v.0.48:

Stogy \Sto"gy\, n.; pl. Stogies. [Written also stogie.]
   [Colloq.]
   1. A stout, coarse boot or shoe; a brogan.
      [Webster 1913 Suppl.]

   2. A kind of cheap, but not necessary inferior, cigar made in
      the form of a cylindrical roll.
      [Webster 1913 Suppl.]

The Collaborative International Dictionary of English v.0.48:

Stogy \Sto"gy\, a. [Etym. uncertain. Cf. Stocky.]
   heavy; coarse; clumsy. [Colloq.]
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

stogy
    n 1: a cheap cigar [syn: stogy, stogie]