We consider three wireless multi-group (MG) multicasting (MC) systems capable of handling heterogeneous user types viz., information decoding (ID) specific users with conventional receiver architectures, energy harvesting (EH) only users with non-linear EH module, and users with joint ID and EH capabilities having separate units for the two operations, respectively. Each user is categorized under unique group(s), which can be of MC type specifically meant for ID users, and/or an energy group consisting of EH explicit users. The joint ID and EH users are a part of both EH group and single MC group. We formulate an optimization problem to minimize the total transmit power with optimal precoder designs for the three aforementioned scenarios, under certain quality-of-service constraints. The problem may be adapted to the well-known semi-definite program and solved via relaxation of rank-1 constraint. However, this process leads to performance degradation in some cases, which increases with the rank of solution obtained from the relaxed problem. Hence, we develop a novel technique motivated by the feasible-point pursuit successive convex approximation method in order to address the rank-related issue. The benefits of proposed method are illustrated under various operating conditions and parameter values, with comparison between the three above-mentioned scenarios.