Under the "dual carbon" goals, rural energy systems urgently need to balance the efficient utilization of renewable energy with the coordinated supply of diverse loads. To address the complex multi-energy coupling relationships (electricity, heat, hydrogen, oxygen) in aquaculture scenarios and the significant seasonal fluctuations of renewable energy, a rural energy system coupling model is developed, integrating photovoltaic, hydropower, biomass, grid, and electrolyzer-hydrogen tank-fuel cell, electrochemical energy storage, and byproduct oxygen utilization components. A multi-objective optimization model is established, aiming to minimize comprehensive costs and maximize overall energy utilization efficiency, with constraints on equipment operation and electro-hydrogen-oxygen-heat balance. At the solution level, an improved NSGA-II method incorporating temporal production simulation is proposed to evaluate the hourly operation process over extended time scales. Using a demonstration zone in southern China as a case study, simulations are conducted over a 552-hour period covering all four seasons. Results show that compared to the baseline scenario S0, the proposed method reduces system operation costs by approximately 12%, increases renewable energy utilization from 91.2% to 98.5%, and achieves an overall energy utilization efficiency of 81%. Additionally, it enables seasonal hydrogen regulation, matches electrolyzer byproduct oxygen with nighttime aeration loads, and synergistically provides heating through biomass and waste heat recovery. The results validate the effectiveness and practical applicability of the proposed method in the clean transition of rural energy systems.