Visible light communication (VLC) is seen as a supplement for fifth-generation (5G) wireless communication in short-range high data rate communication applications [1]. A reliable VLC system relies on an accurate estimate of the position and orientation of the receiver, which corresponds to the six-dimensional positioning problem mentioned in [2]. In this paper, we investigate the simultaneous position and orientation estimation (SPO) problem using received signal strength (RSS), for a visible light system containing multiple LEDs and multiple photodiodes (PDs) (MLMP). Although in general, the position and orientation of the receiver can be represented by a vector and a rotation matrix, respectively, the constraints imposed by the rotation matrix make the numerical optimization in the estimation process cumbersome, e.g, the commonly used constrained optimization method is often very complex and non-robust. Therefore, in this paper, we design two SPO algorithms using the principle of optimization on manifolds, which alleviates the constraints from the rotation matrix. In addition, we propose an initialization algorithm, based on the direct linear transformation (DLT) principle, to obtain an initial estimate in closed-form for the iterative algorithms. To evaluate the performance of the proposed RSS-based SPO algorithms, we derive the Cramer-Rao bound (CRB). In particular, the orientation error component of the CRB corresponds to the intrinsic CRB or the CRB on manifolds, which measures the error in the estimated rotation matrix in a physically meaningful way. Finally, computer simulations show an asymptotic tightness between the performance of the proposed algorithms and the theoretical lower bound, demonstrating the effectiveness of the proposed solutions.