Flux-integrated semiexclusive differential cross sections for charged-current quasielastic and neutral-current elastic neutrino scattering on argon are analyzed. The cross sections are calculated using the relativistic distorted-wave impulse approximation with values of the nucleon axial mass ${M}_{A}=1\text{ }\text{ }\mathrm{GeV}$ and 1.2 GeV. The elastic scattering cross sections are also computed for different strange quark contributions to the neutral-current axial form factor. The flux-integrated differential cross sections as functions of reconstructed neutrino energy are evaluated for the far detector of the SBN experiment. The effects of the short baseline neutrino oscillations are taken into account in a $3+1$ framework. We found that cross sections depend on oscillation parameters and the ratio of the measured and predicted cross sections can be used in a sterile neutrino oscillation study.