With the increasing utilization of electronic equipment in the power system, sub-synchronous oscillation (SSO) has occurred many times and caused off-grid accidents because of power oscillation. SSO has become one of the main problems that restrict the development of new energy. In this paper, power oscillation in grid-side converters (GSCs) in doubly-fed induction generators (DFIGs) under SSO is studied. Firstly, the influence mechanism of SSO on GSC multipath disturbance is studied. Secondly, the problem of coupling oscillation caused by PLL output errors after coordinate transformation is studied, and the mathematical model of GSC output power considering SSO multipath disturbance is established. By analyzing the oscillation suppression ability of the quasi-resonant controller under variable SSO states, the key influencing factors of SSO for GSC power oscillation suppression strategies are determined. Furthermore, based on the above theoretical analysis and research, an improved PLL is designed to eliminate the influence of its output errors on the disturbance of GSC. At the same time, a DFIG-GSC power oscillation suppression strategy using an adaptive quasi-resonant controller is designed to eliminate the influence of SSO on the multi-path disturbance of GSC. Finally, the effectiveness of the proposed suppression strategy is verified using simulation and experimental results.