  We derive a bound on the energy of the general (p,q)-supersymmetric
two-dimensional massive sigma model with torsion, in terms of the topological
and Noether charges that appear as central charges in its supersymmetry
algebra.The bound is saturated by soliton solutions of first-order
Bogomol'nyi-type equations. This generalizes results obtained previously for
p=q models without torsion. We give examples of massive (1,1) models with
torsion that have a group manifold as a target space. We show that they
generically have multiple vacua and find an explicit soliton solution of an
SU(2) model. We also construct a new class of zero torsion massive (4,4) models
with multiple vacua and soliton solutions. In addition, we compute the metrics
on the one-soliton moduli spaces for those cases for which soliton solutions
are known explicitly, and discuss their interpretation.
