In this paper, the minimization of the weighted sum average age of information (AoI) in a multi-source status update communication system is studied. Multiple independent sources send update packets to a common destination node in a time-slotted manner under the limit of maximum retransmission rounds. Different multiple access schemes, i.e., orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are exploited here over a block-fading multiple access channel (MAC). Constrained Markov decision process (CMDP) problems are formulated to describe the AoI minimization problems considering both transmission schemes. The Lagrangian method is utilised to convert CMDP problems to unconstraint Markov decision process (MDP) problems and corresponding algorithms to derive the power allocation policies are obtained. On the other hand, for the case of unknown environments, two online reinforcement learning approaches considering both multiple access schemes are proposed to achieve near-optimal age performance. Numerical simulations validate the improvement of the proposed policy in terms of weighted sum AoI compared to the fixed power transmission policy, and illustrate that NOMA is more favorable in case of larger packet size.