  The anholonomic frame method is generalized for non--Riemannian gravity
models defined by string corrections to the general relativity and
metric-affine gravity (MAG) theories. Such spacetime configurations are modeled
as metric-affine spaces provided with generic off-diagonal metrics (which can
not be diagonalized by coordinate transforms) and anholonomic frames with
associated nonlinear connection (N-connection) structure. We investigate the
field equations of MAG and string gravity with mixed holonomic and anholonomic
variables. There are proved the main theorems on irreducible reduction to
effective Einstein-Proca equations with respect to anholonomic frames adapted
to N-connections. String corrections induced by the antisymmetric H-fields are
considered. There are also proved the theorems and criteria stating a new
method of constructing exact solutions with generic off-diagonal metric ansatz
depending on 3-5 variables and describing various type of locally anisotropic
gravitational configurations with torsion, nonmetricity and/or generalized
Finsler-affine effective geometry. We analyze solutions, generated in string
gravity, when generalized Finsler-affine metrics, torsion and nonmetricity
interact with three dimensional solitons.
