Recently, there have been renewed interests in applying machine learning (ML) techniques to wireless systems. Nevertheless, ML-based approaches often require a large amount of data in training, and prior ML-based MIMO symbol detectors usually adopt offline learning approaches, which are not applicable to real-time signal processing. This paper adopts echo state network (ESN), a prominent type of reservoir computing (RC), to the real-time symbol detection task in MIMO-OFDM systems. Two novel ESN training methods, namely recursive-least-square and generalized adaptive weighted recursive-least-square, are introduced to enhance the performance of ESN training. Furthermore, a decision feedback mechanism is adopted to improve training efficiency and BER performance. Simulation studies show that the proposed methods perform better than previous conventional and ML-based MIMO symbol detectors. Finally, the effectiveness of our RC-based approach is validated with a software-defined radio (SDR) transceiver and extensive field tests in various real-world scenarios. To the best of our knowledge, this is the first real-time SDR implementation for ML-based MIMO-OFDM symbol detectors. Our work strongly indicates that ML-based signal processing could be a promising and critical approach for future wireless networks.