The key to developing future generations of wireless communication systems lies in the expansion of extant methodologies, which ensures the coexistence of a variety of devices within a system. In this paper, we assume several multicasting (MC) groups comprising three types of heterogeneous users including Information Decoding (ID), Energy Harvesting (EH) and both ID and EH. We present a novel framework to investigate the multi-group (MG) - MC precoder designs for three different scenarios, namely, Separate Multicast and Energy Precoding Design (SMEP), Joint Multicast and Energy Precoding Design (JMEP), and Per-User Information and/or Energy Precoding Design (PIEP). In the considered system, a multi-antenna source transmits the relevant information and/or energy to the groups of corresponding receivers using more than one MC streams. The data processing users employ the conventional ID receiver architectures, the EH users make use of a non-linear EH module for energy acquisition, while the users capable of performing both ID and EH utilize the separated architecture with disparate ID and non-linear EH units. Our contribution is threefold. Firstly, we propose an optimization framework to i) minimize the total transmit power and ii) to maximize the sum harvested energy, the two key performance metrics of MG-MC systems. The proposed framework allows the analysis of the system under arbitrary given quality of service and harvested energy requirements. Secondly, to deal with the non-convexity of the formulated problems, we transform the original problems respectively into equivalent forms, which can be effectively solved by semi-definite relaxation (SDR) and alternating optimization. The convergence of the proposed algorithms is analytically guaranteed. Thirdly, a comparative study between the proposed schemes is conducted via extensive numerical results, wherein the benefits of adopting SMEP over JMEP and PIEP models are discussed.