A study of the inelastic scattering of neutrons with an energy of MeV on the nuclei of oxygen, phosphorus, and sulfur was performed at the TANGRA facility at JINR (Dubna). The experiment aimed to refine existing data and obtain new data on the yields and angular distributions of γ-quanta emitted by the studied nuclei due to neutron-induced nuclear reactions using the tagged neutron method. Two types of detector systems were used to register γ-quanta. The γ-ray yields were measured using a high-purity germanium (HPGe) detector. The angular distributions of γ-rays were obtained using a system of 18 scintillation detectors based on bismuth germanite Bi Ge O (BGO) located around the sample. The performed experiments measured the yields of two transitions for the reaction of tagged neutrons with O, nine transitions for the reaction with P, and nine transitions for the reaction with S for the first time. The angular anisotropy of the γ-radiation accompanying the inelastic scattering of neutrons with an energy of MeV on P nuclei was also measured for the first time.