In this paper, we propose a three-stage unified channel estimation strategy for reconfigurable intelligent surface (RIS)-aided multi-user (MU) multiple-input multiple-output (MIMO) millimeter wave (mmWave) systems with the existence of the direct channels, where the base station (BS), the users and the RIS are equipped with uniform planar array (UPA). The effectiveness of the developed three-stage strategy stems from the careful design of both the pilot signal sequence of the users and the vectors of RIS. Specifically, in Stage I, the cascaded channel components are eliminated by configuring the RIS phase shift vectors with a π difference to estimate the direct channels for all users. The orthogonal subspace projection is employed in Stage II to obtain equivalent signal matrices, enabling the estimation of angles of departure (AoDs) of the user-RIS channel for all users. In Stage III, we combine the signals of the time slots with the same pilots and project obtained measurement matrix to the orthogonal complement space of the component consisting of the portion of the direct channel, which removes the direct components and thus prevents error propagation from the direct channels to the cascaded channels. Then, we estimate the angles of arrival (AoAs) of the RIS-BS channel and remaining parameters of the cascaded channel for all users by exploiting the sparsity and correlation in the obtained equivalent matrices. Simulation results demonstrate that the proposed method yields better estimation performance than the existing methods.