This study addresses the challenge of optimizing control strategies for multi-energy systems in high-density residential buildings, focusing on space heating and domestic hot water applications in cold climates. Due to constrained space, dispersed energy consumption patterns, and limited renewable energy integration in such buildings, a multi-energy system combining solar thermal collectors, air source heat pumps, and sewage source heat pumps with an embedded stratified thermal storage tank is proposed. A novel quality-quantity regulation strategy for the demand side dynamically adjusts both the circulating flow rate and temperature of the heating fluid based on tank energy status and load requirements, enhancing energy utilization and extending heat pump operation compared to traditional constant-flow quality regulation. For the supply side, dead-zone control strategies are optimized for each subsystem: solar collectors (upper/lower dead-band temperature difference), air source heat pumps (control based on supply-required temperature difference), and other. Simulation results demonstrate that the quality-quantity strategy better matches heating loads, improves tank stratification, and increases heat pump runtime. Solar subsystem performance is highly sensitive to the upper dead-band limit, while sewage source heat pumps control has minimal impact on solar operation. The findings provide practical guidance for multi-energy system control design, improving efficiency and reducing auxiliary heating dependence in residential buildings.