The convergence of transformative technologies, including the Internet of Things (IoT), Big Data, and Artificial Intelligence (AI), has driven private edge cloud systems to the forefront of research efforts. The access to massive terminals and the emergence of personalized services pose serious challenges for efficient resource management in power private edge cloud systems. To address the challenge of inequitable resource allocation in the private edge cloud, this work proposes an intelligent resource allocation strategy with a slicing and auction approach. By formalizing the resource allocation problem as a Mixed Integer Nonlinear Programming (MINLP) puzzle, the method transforms it into a hierarchical allocation challenge for Mobile Network Operators (MNOs), Mobile Virtual Network Operators (MVNOs), and power terminals. The proposed Multi-hop Progressive Auction Algorithm (MPAA) addresses the sliced resource allocation problem between MNOs and MVNOs. Furthermore, a Terminal Resource Allocation Strategy (TRAS) based on improved particle swarm optimization is proposed to solve the spectrum resource allocation problem between MVNOs and power terminals. Extensive simulation results show that the bidding overhead of MPAA is reduced by 6.12% and the average terminal satisfaction of TRAS is improved by about 1.3% compared to conventional methods, thus improving the utilization of wireless resources within the power AIoT.