In this paper, I address the oscillation probability of O(GeV) neutrinos of
all active flavours produced inside the Sun and detected at the Earth. Flavours
other than electron-type neutrinos may be produced, for example, by the
annihilation of WIMPs which may be trapped inside the Sun. In the GeV energy
regime, matter effects are important both for the ``1-3'' system and the
``1-2'' system, and for different neutrino mass hierarchies. A numerical scan
of the multidimensional three-flavour parameter space is performed,
``inspired'' by the current experimental situation. One important result is
that, in the three-flavour oscillation case, P{alpha,beta} is different from
P{beta,alpha} for a significant portion of the parameter space, even if there
is no CP-violating phase in the MNS matrix. Furthermore, P{mu,mu} has a
significantly different behaviour from P{tau,tau}, which may affect
expectations for the number of events detected at large neutrino telescopes.Comment: 38 pages, 10 figure