In this paper, we present a deep neural network (DNN) based transceiver architecture for delay-Doppler (DD) channel training and detection of orthogonal time frequency space (OTFS) modulation signals along with IQ imbalance (IQI) compensation. The proposed transceiver learns the DD channel over a spatial coherence interval and detects the information symbols using a single DNN trained for this purpose at the receiver. The proposed transceiver also learns the IQ imbalances present in the transmitter and receiver and effectively compensates them. The transmit IQI compensation is realized using a single DNN at the transmitter which learns and provides a compensating modulation alphabet (to pre-rotate the modulation symbols before sending through the transmitter) without explicitly estimating the transmit gain and phase imbalances. The receive IQI imbalance compensation is realized using two DNNs at the receiver, one DNN for explicit estimation of receive gain and phase imbalances and another DNN for compensation. Simulation results show that the proposed DNN-based architecture provides very good performance, making it as a promising approach for the design of practical OTFS transceivers.