With the development of renewable energy technology and communication technology in recent years, many residents now utilize renewable energy devices in their residences with energy storage systems. We have full confidence in the promising prospects of sharing idle energy with others in a community. However, it is a great challenge to share residents’ energy with others in a community to minimize the total cost of all residents. In this paper, we study the problem of energy management and task scheduling for a community with renewable energy and residential cogeneration, such as residential combined heat and power system (resCHP) to pay the least electricity bill. We take elastic and inelastic load demands into account which are delay intolerant and delay tolerant tasks in the community. The minimum cost problem of a non-cooperative community is extracted into a random non-convex optimization problem with some physical constraints. Our objective is to minimize the time-average cost for each resident in the community, including the cost of the external grid and natural gas. The Lyapunov optimization theory and a primal-dual gradient method are adopted to tackle this problem, which needs no future data and has low computational complexity. Furthermore, we design a cooperative renewable energy sharing algorithm based on State-action-reward-state-action (Sarsa) Algorithm, in the condition that each residence in the community is able to communicate with its neighbors by a central controller. Finally, extensive simulations are presented to validate the proposed algorithms by using practical data.