A complete choice of generators of the center of the enveloping algebras of
real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is
obtained in a unified setting. The results simultaneously include the well
known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as
well as the Casimirs for many non-simple algebras such as the inhomogeneous
$iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by
contraction(s) starting from the simple algebras $so(p,q)$. The dimension of
the center of the enveloping algebra of a quasi-simple orthogonal algebra turns
out to be the same as for the simple $so(p,q)$ algebras from which they come by
contraction. The structure of the higher order invariants is given in a
convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski"
elements in the enveloping algebras. As an example showing this approach at
work, the scheme is applied to recovering the Casimirs for the (3+1)
kinematical algebras. Some prospects on the relevance of these results for the
study of expansions are also given.