  Adopting the 3+1 neutrino mixing parameters by the IceCube and shortbase line
experiments, we investigate the sterile-active neutrino oscillation effects on
the supernova neutrino process. For the sterile neutrino ($\nu_s$), we study
two different luminosity models. First, we presume that the $\nu_s$ does not
interact with other particles through the standard interactions apart from the
oscillation with the active neutrinos. Second, we consider that $\nu_s$ can be
directly produced by $\nu_e$ scattering with matter. In both cases, we find
that the pattern of neutrino oscillations can be changed drastically by the
$\nu_s$ in supernova environments. Especially multiple resonances occur, and
consequently affect thermal neutrino-induced reaction rates. As a result,
$^7$Li, $^7$Be, $^{11}$B, $^{11}$C, $^{92}$Nb, $^{98}$Tc and $^{138}$La yields
in the $\nu$-process are changed. Among those nuclei, $^7$Li and $^{11}$B
yields can be constrained by the analysis of observed SiC X grains. Based on
the meteoritic data, we conclude that the second model can be allowed while
first model is excluded. The viability of the second model depends on the
sterile neutrino temperature and the neutrino mass hierarchy.
