With the increasing adoption of cloud-edge collaborative computing in delay-sensitive applications, sleep control of edge nodes has become a key approach to reducing operational energy consumption. However, existing schemes have not balanced energy efficiency and performance under edge node sleep control and still lack a joint optimization mechanism for computation offloading and resource allocation. This paper tackles the problem of optimizing energy-efficient computation offloading and resource allocation (CORA) in cloud-edge collaborative computing systems, where edge servers can dynamically enter sleep mode to reduce power consumption. We model the problem as a mixed-integer nonlinear programming formulation, with the objective of minimizing a weighted sum of overall task latency and the cumulative energy consumption of all IoT devices and edge servers. To handle the hybrid nature of discrete and continuous decision variables and the complex system dynamics, we reformulate the problem for each device as a Markov Decision Process and develop a deep deterministic policy gradient with multi-agent algorithm tailored for such hybrid action spaces. Simulation results show that the proposed CORA strategy achieves superior performance compared to three benchmark schemes with reduced latency and energy consumption.