We investigate the neutrino flavor change effects due to neutrino self-interaction and shock wave propagation, as well as the matter effects on the neutrino process in core-collapsing supernovae (CCSNe). For the hydrodynamics, we use two models: a simple thermal bomb model and a specified hydrodynamics model for SN1987A. For the presupernova model, we take an updated model, adjusted to explain SN1987A, which employs recent developments in the (n, gamma) reaction rates for nuclei near the stability line (A similar to 100). As for the neutrino luminosity, we adopt two different models: equivalent neutrino luminosity and nonequivalent luminosity models. The latter is taken from a synthetic analysis of CCSN simulation data, which quantitatively presented the results obtained by various neutrino transport models. Relevant neutrino-induced reaction rates are calculated using a shell model for light nuclei and a quasiparticle random phase approximation model for heavy nuclei. For each model, we present abundances of the light nuclei (Li-7, Be-7, B-11, and C-11) and the heavy nuclei (Nb-92, Tc-98, La-138, and Ta-180) produced by the neutrino process. The light nuclei abundances turn out to be sensitive to the Mikheyev-Smirnov-Wolfenstein (MSW) region around O-Ne-Mg layer while the heavy nuclei are mainly produced prior to the MSW region. Through detailed analyses, we find that neutrino self-interaction becomes a key ingredient, in addition to the MSW effect, for understanding the neutrino process and the relevant nuclear abundances. The normal mass hierarchy is shown to be more compatible with the meteorite data. The main nuclear reactions for each nucleus are also investigated in detail.