Addressing the challenges of high energy consumption and low efficiency in integrated energy systems, this research develops an optimal scheduling strategy that takes into account the dynamic operational conditions of the system and the complementary nature of electricity, hydrogen, and heat energies. Through the innovative application of variable efficiency gas turbines and solid oxide batteries, our model adeptly converts between these forms of energy. Moreover, we introduce a demand response strategy that seeks to balance efficiency with low-carbon generation and integrates a tiered carbon trading scheme to influence user electricity use and curb system-wide carbon footprints. Empirical results validate the effectiveness of our method in significantly enhancing energy use efficiency, cost savings, and emissions reductions.