  Arbitrary diffeomorphically invariant metric-torsion theories of gravity are
considered. It is assumed that Lagrangians of such theories contain derivatives
of field variables (tensor densities of arbitrary ranks and weights) up to a
second order only. The generalized Klein-Noether methods for constructing
manifestly covariant identities and conserved quantities are developed.
Manifestly covariant expressions are constructed without including auxiliary
structures like a background metric. In the Riemann-Cartan space, the following
\emph{manifestly generally covariant results} are presented: (a) The complete
generalized system of differential identities (the Klein-Noether identities) is
obtained. (b) The generalized currents of three types depending on an arbitrary
vector field displacements are constructed: they are the canonical Noether
current, symmetrized Belinfante current and identically conserved
Hilbert-Bergmann current. In particular, it is stated that the symmetrized
Belinfante current does not depend on divergences in the Lagrangian. (c) The
generalized boundary Klein theorem (third Noether theorem) is proved. (d) The
construction of the generalized superpotential is presented in details, and
questions related to its ambiguities are analyzed.
