Differential space time block coding (STBC) achieves full spatial diversity and avoids channel estimation overhead. Over highly frequency-selective channels, STBC is integrated with orthogonal frequency division multiplexing (OFDM) to efficiently mitigate intersymbol interference effects. However, low-cost implementation of STBC-OFDM with direct-conversion transceivers is sensitive to In-phase/Quadrature-phase imbalance (IQI). In this paper, we quantify the performance impact of IQI at both the transmitter and receiver radio frequency front-ends on differential STBC-OFDM systems which has not been investigated before in the literature. In addition, we propose a widely-linear compensation algorithm at the receiver to mitigate the performance degradation caused by the IQI at the transmitter and receiver ends. Moreover, a parameter-based generalized algorithm is proposed to extract the IQI parameters and improve the performance under high-mobility. The adaptive compensation algorithms are blind and work in a decision-directed manner without using known pilots or training sequences. Numerical results show that our proposed compensation algorithms can effectively mitigate IQI in differential STBC-OFDM.