The large-scale integration of renewable energy sources, such as wind power and solar power, into the power system has significantly transformed its characteristics. The issue of sub-synchronous oscillation (SSO) becomes increasingly prominent, severely impacting the system stability. As the wind turbines vary in structures and parameters, existing model-based SSO suppression approaches do not fully consider wind turbine differences and multi-mode oscillation frequencies. To address these issues, this paper proposes a decentralized SSO suppression controller for doubly-fed induction generator (DFIG)-based wind farms using periodic updating data-enabled predictive control (PUDeePC) approach. Firstly, to better adapt to the time-varying system and external disturbance, a periodic updating algorithm is proposed incorporating anomaly detection. The stability of the PUDeePC approach is theoretically validated, and its robustness to variations and disturbances is qualitatively analyzed. Finally, the effectiveness of the PUDeePC approach is revealed through numerical simulations under various conditions, including compensation level variation, wind power output variation, number of online DFIG variations, multi-mode SSOs, and asynchronous PUDeePC approach.