To alleviate the high peak-to-average power ratio (PAPR), high complexity in user terminal and sensitivity to carrier frequency offset (CFO) problems in current orthogonal frequency division multiple access (OFDMA) systems, a Quadrature OFDM (Q-OFDMA) system has been recently proposed in the single-input single-output environment. In this paper we study the realization of multi-input multi-output (MIMO) diversity- and multiplexing- oriented methods for Q-OFDMA systems. An Alamouti-like space-time block code (STBC) and simple detection for spatial multiplexing (SM) for Q-OFDMA systems are constructed, both zero forcing (ZF) and minimum mean square error (MMSE) equalizers are investigated. The proposed STBC is a full diversity scheme, which encodes in intermediate domain and decodes in frequency domain. Analytical and empirical results demonstrate that the Q-OFDMA systems can be implemented flexibly and efficiently in a MIMO framework, and the proposed scheme can be easily applied in OFDMA and Single-Carrier Frequency Division Multiple Access (SC-FDMA) by adjusting the parameters of Q-OFDMA.