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Due to environmental issues and smart grid development, distributed energy resources, energy storage systems, and demand response (DR) are gaining attention to reduce the pollution and fossil fuel usage. This paper presents a customer’s preferences based innovative home appliances scheduling framework considering numerous constraints and DR for scheduling household appliances incorporating local energy grid and energy storage systems, including electrical and thermal energy storage. First, the models of household appliances and air conditioning load are built as the shiftable and non-schedulable loads and a flexible thermal load, respectively. Second, an enhanced normalized normal constraint (ENNC) strategy based on game theory (GT) is presented for a novel home appliance scheduling (HAS) framework with the objectives to optimize consumption cost, end-users comfort, and peak to average ratio. Then, the fuzzy compromising (FCP) method is proposed to optimize overall energy cost and gaseous emissions for the novel HAS framework with a residential local energy grid. In addition to this, conditional value at risk (CVaR) has also been incorporated in the objective function to resolve the sudden absence of distributed energy resources and power failures. Finally, case studies on data from Dallas, Texas, USA are performed, and the simulation results show that the proposed strategy is computationally inexpensive and outperforms other approaches in terms of electricity cost, gaseous emissions, and customer’s comfort. The proposed approach gives a significantly lower cost of 104.30 cents and gaseous emissions of about 18.753 kg for an entire day of novel HAS with DR adoption. Thus, it can provide help for DR accomplishment and precise prediction of electricity consumption.