  We study spin oscillations of massive Dirac neutrinos in background matter,
electromagnetic and gravitational fields. First, using the Dirac equation for a
neutrino interacting with the external fields in curved spacetime, we rederive
the quasiclassical equation for the neutrino spin evolution, which was proposed
previously basing on principles of the general covariance. Then, we apply this
result for the description of neutrino spin oscillations in nonmoving and
unpolarized matter under the influence of a constant transverse magnetic field
and a gravitational wave. We derive the effective Schr\"odinger equation for
neutrino oscillations in these external fields and solve it numerically.
Choosing realistic parameters of external fields, we show that the parametric
resonance can take place in spin oscillations of low energy neutrinos. Some
astrophysical applications are briefly discussed.
