In this study, we investigate hybrid utilization of angle-of-arrival (AOA) and received signal strength (RSS) information in visible light communication (VLC) systems for 3D localization. We show that AOA-based localization method allows the receiver to locate itself via a least squares estimator by exploiting the directionality of light-emitting diodes (LEDs). We then prove that when the RSS information is taken into account, the positioning accuracy of AOA-based localization can be improved further using a weighted least squares solution. On the other hand, when the radiation patterns of LEDs are explicitly considered in the estimation, RSS-based localization yields highly accurate results. In order to deal with the system of nonlinear equations for RSS-based localization, we develop an analytical learning rule based on the Newton-Raphson method. The non-convex structure is addressed by initializing the learning rule based on 1) location estimates, and 2) a newly developed method, which we refer as random report and cluster algorithm. As a benchmark, we also derive analytical expression of the Cramer-Rao lower bound (CRLB) for RSS-based localization, which captures any deployment scenario positioning in 3D geometry. Finally, we demonstrate the effectiveness of the proposed solutions for a wide range of LED characteristics and orientations through extensive computer simulations.