With the popularity of multimedia sensing at cloud edges and the reducing cost of the Internet of Things (IoTs) fog devices and systems, new challenges have been posed to efficiently deal with the big data multimedia traffic generated from IoT sensing units. Specifically, in this paper we introduce the concept of Multimedia Sensing as a Service (MSaaS), and propose a generalized premium prioritization-based Quality of Experience (QoE) paradigm for wireless big-volumes-of-data (B-VD) multimedia communications, with significant energy saving potentials for future multimedia IoT devices and systems. The key contribution of this new framework is its data diversity flexibility at the application layer, which could be flexibly adopted by future multimedia communication systems. Data dependencies in spatial, frequency and temporal domains are analyzed, and interaction with uplink resource allocation optimization are investigated with regards to wireless communication energy cost estimation. Extensive simulation results demonstrate that the proposed prioritization-based communication paradigm has significant energy saving potentials for BVD MSaaS wireless multimedia communications at cloud edges and fogs.