The rapid advancement of modular multi-level converter-based high-voltage direct current (MMC-HVDC) interconnection projects may lead to torsional vibrations in turbo-generator shafts, causing oscillations that pose operational risks to the power system. Impedance-based analysis is an effective method to evaluate the stability of power systems with power electronic components. However, conventional turbo-generator impedance models, such as the RL equivalent impedance model, only address the electrical aspects of turbo-generators and neglect the influence of shafting characteristics, potentially leading to inaccurate analysis results. To address this issue, a turbo-generator impedance model is introduced which incorporates shafting characteristics validated through frequency scanning methods. Focusing on the turbo-generator and MMC-HVDC interconnection system, the oscillation analysis results are compared using the developed and traditional impedance models. The findings indicate that the developed model exhibits greater applicability and accuracy for power systems incorporating electronic equipment. Furthermore, a virtual damping control strategy for MMC-HVDC based on modulation links is developed to mitigate oscillation issues. The efficacies of the proposed impedance model and control strategy are validated in the turbo-generator and MMC-HVDC interconnection system.