  Neutrino-induced reactions on $^{16}$O are investigated by shell-model
calculaions with new shell-model Hamiltonians, which can describe well the
structure of $p$-shell and $p$-$sd$ shell nuclei. Distribution of the
spin-dipole strengths in $^{16}$O, which give major contributions to the
$\nu$-$^{16}$O reaction cross sections, is studied with the new Hamiltonians.
Muon-capture reaction rates on $^{16}$O are also studied to discuss the
quenching of the axial-vector coupling in nuclear medium. Charged-current and
neutral-current reaction cross sections are evaluated in various particle and
$\gamma$ emission channels as well as the total ones at neutrino energies up to
$E_{\nu}\approx$ 100 MeV. Branching ratios for the various channels are
obtained by the Hauser-Feshbach statistical model calculations, and partial
cross sections for single- and multi-particle emission channels are evaluated.
The cross sections updated are compared with previous continuum random phase
approximation (CRPA) calculations. Effects of multi-particle emission channels
on nucleosynthesis in core-collapse supernova (SN) explosions are investigated.
Inclusion of $\alpha$p emission channels is found to lead to an enhancement of
production yields of $^{11}$B and $^{11}$C through $^{16}$O ($\nu$, $\nu$'
$\alpha$p) $^{11}$B and $^{16}$O ($\nu$, e$^{-}$ $\alpha$p) $^{11}$C reactions,
respectively.
