This paper studies a novel movable antenna (MA)-enhanced multiuser multiple-input multiple-output downlink system designed to improve wireless communication performance. We aim to maximize the average achievable sum rate through two-timescale optimization exploiting instantaneous channel state information at the receiver (I-CSIR) for receive antenna position vector (APV) design and statistical channel state information at the transmitter (S-CSIT) for transmit APV and covariance matrix design. We first decompose the resulting stochastic optimization problem into a series of short-term problems and one long-term problem. Then, a gradient ascent algorithm is proposed to obtain suboptimal receive APVs for the short-term problems for given I-CSIR samples. Based on the output of the gradient ascent algorithm, a series of convex objective/feasibility surrogates for the long-term problem are constructed and solved utilizing the constrained stochastic successive convex approximation (CSSCA) algorithm. Furthermore, we propose a planar movement mode for the receive MAs to facilitate efficient antenna movement and the development of a low-complexity primal-dual decomposition-based stochastic successive convex approximation (PDD-SSCA) algorithm, which finds Karush-Kuhn-Tucker (KKT) solutions almost surely. Our numerical results reveal that, for both the general and the planar movement modes, the proposed two-timescale MA-enhanced system design significantly improves the average achievable sum rate and the feasibility of the formulated problem compared to benchmark schemes.