The rapid growth of private car ownership has worsened the urban parking predicament, underscoring the need for accurate and effective parking availability prediction to support urban planning and management. To address key limitations in modeling spatio-temporal dependencies and exploiting multi-source data for parking availability prediction, this study proposes a novel approach with SST-iTransformer. The methodology leverages K-means clustering to establish parking cluster zones (PCZs), extracting and integrating traffic demand characteristics from various transportation modes (i.e., metro, bus, online ride-hailing, and taxi) associated with the targeted parking lots. Upgraded on vanilla iTransformer, SST-iTransformer integrates masking-reconstruction-based pretext tasks for self-supervised spatio-temporal representation learning, and features an innovative dual-branch attention mechanism: Series Attention captures long-term temporal dependencies via patching operations, while Channel Attention models cross-variate interactions through inverted dimensions. Extensive experiments using real-world data from Chengdu, China, demonstrate that SST-iTransformer outperforms baseline deep learning models (including Informer, Autoformer, Crossformer, and iTransformer), achieving state-of-the-art performance with the lowest mean squared error (MSE) and competitive mean absolute error (MAE). Comprehensive ablation studies quantitatively reveal the relative importance of different data sources: incorporating ride-hailing data provides the largest performance gains, followed by taxi, whereas fixed-route transit features (bus/metro) contribute marginally. Spatial correlation analysis further confirms that excluding historical data from correlated parking lots within PCZs leads to substantial performance degradation, underscoring the importance of modeling spatial dependencies.