A critical concern within the realm of visible light communications (VLC) pertains to enhancing system data rate, particularly in scenarios where the direct line-of-sight (LoS) connection is obstructed by obstacles. The deployment of meta-surface-based simultaneous transmission and reflection reconfigurable intelligent surface (STAR-RIS) has emerged to combat challenging LoS blockage scenarios and to provide 360 coverage in radio-frequency wireless systems. Recently, the concept of optical simultaneous transmission and reflection reconfigurable intelligent surface (OSTAR-RIS) has been promoted for VLC systems. This work is dedicated to studying the performance of OSTAR-RIS in detail and unveiling the VLC system performance gain under such technology. Specifically, we propose a novel multi-user indoor VLC system that is assisted by OSTAR-RIS. To improve the sum rate performance of the proposed system, both power-domain non-orthogonal multiple access (NOMA) and rate splitting multiple access (RSMA) are investigated in this work. To realize this, a sum rate maximization problem that jointly optimizes the roll and yaw angles of the reflector elements as well as the refractive index of the refractor elements in OSTAR-RIS is formulated, solved, and evaluated. The maximization problem takes into account practical considerations, such as the presence of non-users (i.e., blockers) and the orientation of the recipient's device. The sine-cosine meta-heuristic algorithm is employed to get the optimal solution of the formulated non-convex optimization problem. Moreover, the study delves into the sum energy efficiency optimization of the proposed system. Simulation results indicate that the proposed OSTAR-RIS RSMA-aided VLC system outperforms the OSTAR-RIS NOMA-based VLC system in terms of both the sum rate and the sum energy efficiency.