  The present paper continues the work of the authors [arXiv:1306.6887
[gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity
presented more concretely, setting that their Lagrangians are \emph{manifestly}
generally covariant scalars. It is assumed that Lagrangians depend on metric
tensor, curvature tensor, torsion tensor and its first and second covariant
derivatives, besides, on an arbitrary set of other tensor (matter) fields and
their first and second covariant derivatives. Thus, both the standard minimal
coupling with the Riemann-Cartan geometry and non-minimal coupling with the
curvature and torsion tensors are considered.
  The studies and results are as follow. (a) A physical interpretation of the
Noether and Klein identities is examined. It was found that they are the basis
for constructing equations of balance of energy-momentum tensors of various
types (canonical, metrical and Belinfante symmetrized). The equations of
balance are presented. (b) Using the generalized equations of balance, new
(generalized) manifestly generally covariant expressions for canonical
energy-momentum and spin tensors of the matter fields are constructed. In the
cases, when the matter Lagrangian contains both the higher derivatives and
non-minimal coupling with curvature and torsion, such generalizations are
non-trivial. (c) The Belinfante procedure is generalized for an arbitrary
Riemann-Cartan space. (d) A more convenient in applications generalized
expression for the canonical superpotential is obtained. (e) A total system of
equations for the gravitational fields and matter sources are presented in the
form more naturally generalizing the Einstein-Cartan equations with matter.
This result, being a one of more important results itself, is to be also a
basis for constructing physically sensible conservation laws and their
applications.
