Omnidirectional videos (ODVs) are redefining viewer experiences in virtual reality (VR) by offering an unprecedented full field-of-view (FOV). This study extends the domain of saliency prediction to 360$^\circ$∘ environments, addressing the complexities of spherical distortion and the integration of spatial audio. Contextually, ODVs have transformed user experience by adding a spatial audio dimension that aligns sound direction with the viewer's perspective in spherical scenes. Motivated by the lack of comprehensive datasets for 360$^\circ$∘ audio-visual saliency prediction, our study curates YT360-EyeTracking, a new dataset of 81 ODVs, each observed under varying audio-visual conditions. Our goal is to explore how to utilize audio-visual cues to effectively predict visual saliency in 360$^\circ$∘ videos. Towards this aim, we propose two novel saliency prediction models: SalViT360, a vision-transformer-based framework for ODVs equipped with spherical geometry-aware spatio-temporal attention layers, and SalViT360-AV, which further incorporates transformer adapters conditioned on audio input. Our results on a number of benchmark datasets, including our YT360-EyeTracking, demonstrate that SalViT360 and SalViT360-AV significantly outperform existing methods in predicting viewer attention in 360$^\circ$∘ scenes. Interpreting these results, we suggest that integrating spatial audio cues in the model architecture is crucial for accurate saliency prediction in omnidirectional videos.