Orbital angular momentum (OAM) has been acknowledged as a potential technology for 6G wireless communication since its mode orthogonality can improve the degree of freedom (DoF) and capacity. In this paper, orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are explored in OAM downlink systems to improve the sum-capacity for the coaxial multi-user scenario. For the OMA-OAM case, a mode selection algorithm is proposed, and a mode-division OAM design can be accomplished by solving an optimization problem with a quality-of-service (QoS) constraint. For the NOMA-OAM case, a non-convex optimization problem is formulated to maximize the sum-capacity, and an iterative algorithm is presented by approximating the capacity as a concave quadratic function in each iteration. By this means, we introduce a computationally tractable successive convex quadratic programming (SCQP) framework to handle the highly non-convex capacity function efficiently. An extension to the non-coaxial case is considered furthermore. Simulation results are provided to confirm the effectiveness of the proposed mode-division OMA-OAM and NOMA-OAM schemes, guaranteeing the superiority compared to conventional OMA-OAM systems.