Within the framework of a relativistic single particle model we calculate neutral- and charged-current reactions for the neutrino scattering on 12 C and 16 O in quasielastic region. In the intermediate neutrino energy (500 MeV), we develop several ways to investigate effects of the strangeness, such as ratios of proton to neutron for neutral-current reaction, ratios of the neutral- to charged-current reactions, and asymmetries by incident neutrino and antineutrino. A cancellation mechanism of the strangeness effects in the nuclei was found to lead to indiscernible strangeness effects on the relevant cross sections. Consequently, the strangeness effects on the asymmetries and ratios are more feasible tools of looking for the strangeness effects rather than those on the cross section. These phenomena are shown to be nearly independent of the target nuclei exploited in this calculation.