In this paper, we propose a cross layer energy efficient resource allocation and remote radio head (RRH) selection algorithm for heterogeneous traffic in power domain-non-orthogonal multiple access (PD-NOMA) based heterogeneous cloud radio access networks (H-CRANs). The main aim is to maximize the EE of the elastic users subject to the average delay constraint of the streaming users and the constraints, RRH selection, subcarrier, transmit power, and successive interference cancellation. The considered optimization problem is non-convex, NP-hard, and intractable. To solve this problem, we transform the fractional objective function into a subtractive form. Then, we utilize successive convex approximation approach. Moreover, in order to increase the processing speed, we introduce a framework for accelerating the successive convex approximation for low complexity with the Lagrangian method on graphics processing unit. Furthermore, in order to show the optimality gap of the proposed successive convex approximation approach, we solve the proposed optimization problem by applying an optimal method based on the monotonic optimization. Studying different scenarios show that by using both PD-NOMA technique and H-CRAN, the system energy efficiency is improved.