Spin−orbit coupling (SOC) combined with electronic correlation can induce topological phase transition, producing novel electronic states. Here, we investigate the impact of SOC combined with correlation effects on physical properties of monolayer OsBr₂, based on first-principles calculations with generalized gradient approximation plus U (GGA+U) approach. With intrinsic out-of-plane magnetic anisotropy, OsBr₂ undergoes threefold topological phase transition with increasing U, and valley-polarized quantum anomalous Hall insulator (VQAHI) to half-valley-metal (HVM) to ferrovalley insulator (FVI) to HVM to VQAHI to HVM to FVI transitions can be induced. These topological phase transitions are connected with sign-reversible Berry curvature and band inversion between \text{textcolor}[RGB]12,108,100d_{xy}/\text{textcolor}[RGB]12,108,100d_{x^2-y^2} and \text{textcolor}[RGB]12,108,100d_{z^2} orbitals. Due to \text{textcolor}[RGB]12,108,100\overline{6}m2 symmetry, piezoelectric polarization of OsBr₂ is confined along the in-plane armchair direction, and only one d₁₁ is independent. For a given material, the correlation strength should be fixed, and OsBr₂ may be a piezoelectric VQAHI (PVQAHI), piezoelectric HVM (PHVM) or piezoelectric FVI (PFVI). The valley polarization can be flipped by reversing the magnetization of Os atoms, and the ferrovalley (FV) and nontrivial topological properties will be suppressed by manipulating out-of-plane magnetization to in-plane one. In considered reasonable U range, the estimated Curie temperatures all are higher than room temperature. Our findings provide a comprehensive understanding on possible electronic states of OsBr₂, and confirm that strong SOC combined with electronic correlation can induce multiple quantum phase transition.