Multi-sensory Extended Reality (mXR) applications represent a cornerstone technology for immersive communications in the 6G and IMT-2030 frameworks, enabling synchronized stimulation across multiple human sensory modalities to create authentic immersive experiences. mXR applications demand simultaneous satisfaction of stringent data rate, delay, and reliability requirements across all sensory streams, necessitating an unprecedented convergence of enhanced Mobile Broadband (eMBB) and Ultra-Reliable Low-Latency Communications (URLLC) service paradigms. Existing 5G scheduling schemes, designed to optimize either eMBB or URLLC services independently and typically handling decoupled data streams, do not address the cross-modal synchronization and joint optimization challenges of mXR applications. This paper proposes \textit{DREAM-X (Delay-Reliability Aware Scheduling for Multi-sensory XR Applications)}, a unified scheduling framework specifically designed for next generation (NextG) networks to support mXR services. This framework includes a novel Multi-modal Delay Tracking Queue architecture that organizes multi-sensory data units based on transmission deadlines, enabling precise cross-modal delay coordination. We formulate the scheduling problem as a constrained optimization and develop a Model Predictive Control (MPC) solution with rolling horizon optimization to ensure computational tractability for real-time deployment. The simulation results show that DREAM-X provides multi-fold gains in the number of satisfied mXR users compared to conventional and state-of-the-art XR scheduling approaches, while maintaining strict delay and reliability constraints.