  Empirically determining the averaged variations of the orbital parameters of
the stars orbiting the Supermassive Black Hole (SBH) hosted by the Galactic
Centre (GC) in Sgr A* is, in principle, a valuable tool to put on the test the
General Theory of Relativity (GTR), in regimes far stronger than those tested
so far, and certain key predictions of it like the no-hair theorems. We
analytically work out the long-term variations of all the six osculating
Keplerian orbital elements of a test particle orbiting a non-spherical,
rotating body with quadrupole moment Q_2 and angular momentum S for a generic
spatial orientation of its spin axis k. This choice is motivated by the fact
that, basically, we do not know the position in the sky of the spin axis of the
SBH in Sgr A* with sufficient accuracy. We apply our results to S2, which is
the closest star discovered so far having an orbital period P_b = 15.98 yr, and
to a hypothetical closer star X with P_b = 0.5 yr. Our calculations are quite
general, not being related to any specific parameterization of k, and can be
applied also to astrophysical binary systems, stellar planetary systems, and
planetary satellite geodesy in which different reference frames, generally not
aligned with the primary's rotational axis, are routinely used.
