Cellular-based networks are deemed as one solution to provide communication links for the internet of things (IoT) due to its high reliability and wide coverage. However, due to the overloaded machine-type devices in IoT, the existing random access procedure in cellular networks suffers significant preamble collision problem and hardly meets the requirement of large random access. Despite the effort to cope with the preamble collision problem in conventional random access control schemes, other important performance requirements in random access are not well addressed, including access delay, energy consumption, and service priority. To improve the random access control scheme, we propose a novel hierarchical hybrid (HH) access class barring (ACB) and back-off (BO) scheme (HH ACB-BO scheme), where the hybrid ACB-BO is exploited to balance the delay-energy tradeoff, and the hierarchical structure is proposed to prioritize communication services. We mathematically formulate this random access control scheme to optimize the delay and energy performance jointly. With the fixed priority weights for each service priority, the closed-form of the optimal ACB factors and BO indicators adjustment result is derived. Moreover, in order to realize the adaptive prioritized random access control, we apply deep reinforcement learning (DRL) to the proposed random access scheme to dynamically adjust the ACB factors and BO indicators in an online manner. Considering the hierarchical structure and the action space complexity in DRL, a multi-agent DRL algorithm is designed for the HH ACB-BO scheme (multi-agent HH-DRL algorithm), where online policy transfer is applied to guarantee the policy effectiveness in the practical networks. Finally, simulation results verify the effectiveness of the proposed HH ACB-BO scheme and reveal that the multi-agent HH-DRL algorithm outperforms other algorithms in terms of average access success probability and energy consumption performance.