  A generalized geometric method is developed for constructing exact solutions
of gravitational field equations in Einstein theory and generalizations. First,
we apply the formalism of nonholonomic frame deformations (formally considered
for nonholonomic manifolds and Finsler spaces) when the gravitational field
equations transform into systems of nonlinear partial differential equations
which can be integrated in general form. The new classes of solutions are
defined by generic off-diagonal metrics depending on integration functions on
one, two and three (or three and four) variables if we consider four (or five)
dimensional spacetimes. Second, we use a general scheme when one (two)
parameter families of exact solutions are defined by any source-free solutions
of Einstein's equations with one (two) Killing vector field(s). A successive
iteration procedure results in new classes of solutions characterized by an
infinite number of parameters for a non-Abelian group involving arbitrary
functions on one variable. Five classes of exact off-diagonal solutions are
constructed in vacuum Einstein and in string gravity describing solitonic
pp-wave interactions. We explore possible physical consequences of such
solutions derived from primary Schwarzschild or pp-wave metrics.
