The proliferation of 5G/B5G communication has led to increased integration between digital twin (DT) technology and connected autonomous vehicular systems (CAVS). The complex and resource-intensive vehicular applications pose significant connectivity and performance challenges for CAVS. To improve connectivity, optimize spectrum allocation, and mitigate network congestion, non-orthogonal multiple access (NOMA) is implemented. Furthermore, offloading and service caching are employed by storing and offloading relevant services at the edge of vehicular networks. However, due to the limited caching storage of vehicular edge servers, the decision to cache popular and emergent services to minimize delay and energy consumption becomes challenging. The decisions regarding computation offloading and service caching are also strongly coupled. In this work, a popularity-conscious service caching and offloading problem (PSCAOP) in a DT and NOMA-aided CAVS (DTCAVS) is studied. PSCAOP is mathematically constructed and observed to be NP-complete. Then a quantum-inspired particle swarm optimization (QPSO) algorithm is proposed for DTCAVS (DTCAVS-QPSO), aiming to minimize delay and energy consumption. DTCAVS-QPSO prioritizes the popular and emergent service caching. The quantum particle (QP) is encoded to provide a comprehensive solution to the PSCAOP. A one-time mapping algorithm is used to decode the QPs. The fitness function is formulated considering delay, energy consumption, and type of service. All the phases of DTCAVS-QPSO are observed to be bounded in polynomial time. The significance of the proposed DTCAVS-QPSO is demonstrated through extensive simulations and hypothesis-based statistical analysis. Experimental outcomes underscore the superiority of the DTCAVS-QPSO over other standard works, indicating an average delay and an energy consumption reduction between 6% and 49%.