  We present the formalism and numerical results for torsional oscillations of
relativistic stars endowed with a strong dipole magnetic field. We do a
systematic search of parameter space by computing torsional mode frequencies
for various values of the harmonic index $\ell$ and for various overtones,
using an extended sample of models of compact stars, varying in mass,
high-density equation of state and crust model. We show that torsional mode
frequencies are sensitive to the crust model if the high-density equation of
state is very stiff. In addition, torsional mode frequencies are drastically
affected by a dipole magnetic field, if the latter has a strength exceeding
roughly $10^{15}$G and we find that the magnetic field effects are sensitive to
the adopted crust model. Using our extended numerical results we derive
empirical relations for the effect of the magnetic field on torsional modes as
well as for the crust thickness. We compare our numerical results to observed
frequencies in SGRs and find that certain high-density EoS and mass values are
favored over others in the non-magnetized limit. On the other hand, if the
magnetic field is strong, then its effect has to be taken into account in
attempts to formulate a theory of asteroseismology for magnetars.
