Integrated sensing and communications (ISAC) is emerging as a key technique for next-generation wireless systems. In order to enable ubiquitous mobile network and widely deployed base stations with radar sensing functionality, using standard multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) transmitter architectures and waveforms to achieve both satisfactory sensing and communication performance is a crucial task for practical implementations of ISAC. In this paper, we propose a novel joint angle-range-velocity estimation algorithm for the considered MIMO-OFDM ISAC system. The approach is based on classical MIMO-OFDM waveforms widely adopted in wireless communications. Specifically, the angle-range-velocity information of potential targets is jointly extracted by utilizing all the received echo signals in a coherent processing interval (CPI). Therefore, the proposed joint estimation algorithm can achieve larger processing gains and higher resolution by fully exploiting echo signals and jointly estimating the angle-range-velocity information. Theoretical analysis for maximum unambiguous range, resolution, and processing gains are provided to verify the advantages of the proposed joint estimation algorithm. Finally, extensive numerical experiments are presented to demonstrate that the proposed estimation approach can achieve significantly lower root-mean-square-error (RMSE) of angle/range/velocity estimation for both single-target and multi-target scenarios.