A novel solid oxide fuel cell (SOFC)-based cogeneration system is proposed here, integrating an organic Rankine cycle for waste heat recovery. Technical–economic and parametric analyses are conducted, and a multi-objective optimization is carried out. The results reveal that the net electrical efficiency, investment cost, and payback time are 56.6%, USD 2,408,256, and 3.27 years, respectively. The parametric analysis indicates that the current density should be limited between 0.3 A/cm2 and 0.9 A/cm2, and the stack temperature should be controlled between 675 °C and 875 °C. After the operational optimization of ηele-CostTCI, the investment cost and the net electrical efficiency are obtained as USD 2,164,742 and 62.1%. After the ηele-PBT optimization, the payback period and the net electrical efficiency are 3.22 years and 58.9%. The heat transfer network optimization achieves the highest efficiency and reduces the cold utilities by 43 kW, but three additional heat exchangers should be added to the system. This research provides practical reference and pragmatic guidance for the integration, analysis, operation, and heat transfer network optimization of SOFC-based cogeneration systems.