Vortex-induced vibrations have a considerable effect on overhead power transmission lines, often leading to fatigue-failure. While nonlinear models exist for power lines, vibration dampers, and vortex-induced vibrations, no work combines the nonlinearities stemming from the cable, vibration damper, and fluid forces in a single model. As power transmission lines are a major component of modern infrastructure, a thorough understanding of the nonlinear dynamic interactions of conductors, dampers, and wind forces is crucial. This paper examines a conductor with attached Stockbridge dampers under vortex-induced vibration. Sources of nonlinearity in this system include mid-plane stretching of the conductor, equivalent cubic stiffness of the Stockbridge damper, and fluctuating lift force modeled as a Van der Pol oscillator. The equations of motion for the resulting system are discretized using Galerkin’s method and solved using the numerical continuation method. Through parametric analysis, the effects of factors such as damper position and mass ratio on system response are determined. Insight is gained on the combined nonlinear system and a strong foundation is formed for ongoing study.