  We find the characteristic identities for the split Casimir operator in the
defining and adjoint representations of the $osp(M|N)$ and $s\ell(M|N)$ Lie
superalgebras. These identities are used to build the projectors onto invariant
subspaces of the representation $T^{\otimes 2}$ of the $osp(M|N)$ and
$s\ell(M|N)$ Lie superalgebras in the cases when $T$ is the defining and
adjoint representations. For defining representations, the $osp(M|N)$- and
$s\ell(M|N)$-invariant solutions of the Yang-Baxter equation are expressed as
rational functions of the split Casimir operator. For the adjoint
representation, the characteristic identities and invariant projectors obtained
are considered from the viewpoint of a universal description of Lie
superalgebras by means of the Vogel parametrization. We also construct a
universal generating function for higher Casimir operators of the $osp(M|N)$
and $s\ell(M|N)$ Lie superalgebras in the adjoint representation.
