The phenomenon of sub-synchronous oscillation (SSO) poses significant threats to the stability of power systems. The advent of artificial intelligence (AI) has revolutionized SSO research through data-driven methodologies, which necessitates a substantial collection of data for effective training, a requirement frequently unfulfilled in practical power systems due to limited data availability. To address the critical issue of data scarcity in training AI models, this paper proposes a novel transfer-learning-based (TL-based) Wasserstein generative adversarial network (WGAN) approach for synthetic data generation of SSO in wind farms. To improve the capability of WGAN to capture the bidirectional temporal features inherent in oscillation data, a bidirectional long short-term memory (BiLSTM) layer is introduced. Additionally, to address the training instability caused by few-shot learning scenarios, the discriminator is augmented with mini-batch discrimination (MBD) layers and gradient penalty (GP) terms. Finally, TL is leveraged to fine-tune the model, effectively bridging the gap between the training data and real-world system data. To evaluate the quality of the synthetic data, two indexes are proposed based on dynamic time warping (DTW) and frequency domain analysis, followed by a classification task. Case studies demonstrate the effectiveness of the proposed approach in swiftly generating a large volume of synthetic SSO data, thereby significantly mitigating the issue of data scarcity prevalent in SSO research.