In this paper, the joint optimization problem with energy efficiency and effective resource utilization is investigated for heterogeneous and distributed multi-core embedded systems. The system model is considered to be fully a heterogeneous model, that is, all nodes have different maximum speeds and power consumption levels from the perspective of hardware while they can employ different scheduling strategies from the perspective of applications. Since the concerned problem by nature is a multi-constrained and multi-variable optimization problem in which a closed-form solution cannot be obtained, our aim is to propose a power allocation and load balancing strategy based on Lagrange theory. Furthermore, when the problem cannot be fully solved by Lagrange approach, a data fitting method is employed to obtain core speed first, and then load balancing schedule is solved by Lagrange method. Several numerical examples are given to show the effectiveness of the proposed method and to demonstrate the impact of each factor to the present optimization system. Finally, simulation and practical evaluations show that the theoretical results are consistent with the practical results. To the best of our knowledge, this is the first work that combines load balancing, energy efficiency, hardware heterogeneity and application heterogeneity in heterogeneous and distributed embedded systems.