In this paper, a novel routing strategy to cater the energy consumption and delay sensitivity issues in deep underwater wireless sensor networks is proposed. This strategy is named as ESDR: Event Segregation based Delay sensitive Routing. In this strategy sensed events are segregated on the basis of their criticality and, are forwarded to their respective destinations based on forwarding functions. These functions depend on different routing metrics like: Signal Quality Index, Localization free Signal to Noise Ratio, Energy Cost Function and Depth Dependent Function. The problem of incomparable values of previously defined forwarding functions causes uneven delays in forwarding process. Hence forwarding functions are redefined to ensure their comparable values in different depth regions. Packet forwarding strategy is based on the event segregation approach which forwards one third of the generated events (delay sensitive) to surface sinks and two third events (normal events) are forwarded to mobile sinks. Motion of mobile sinks is influenced by the relative distribution of normal nodes. We have also incorporated two different mobility patterns named as; adaptive mobility and uniform mobility for mobile sinks. The later one is implemented for collecting the packets generated by the normal nodes. These improvements ensure optimum holding time, uniform delay and in-time reporting of delay sensitive events. This scheme is compared with the existing ones and outperforms the existing schemes in terms of network lifetime, delay and throughput.