Omnidirectional video (ODV) can provide an immersive experience and is widely utilized in the field of virtual reality and augmented reality. However, the restricted capturing devices and transmission bandwidth lead to the low resolution of ODVs. Video super-resolution (VSR) methods are proposed to enhance the resolution of videos, but ODV projection distortions in the application are not well addressed directly applying such methods. To achieve better super-resolution reconstruction quality, we propose a novel Spatio-Temporal Distortion Aware Network (STDAN) oriented to ODV characteristics. Specifically, a spatio-temporal distortion modulation module is introduced to improve spatial ODV projection distortions and exploit the temporal correlation according to intra and inter alignments. Next, we design a multi-frame reconstruction and fusion mechanism to refine the consistency of reconstructed ODV frames. Furthermore, we incorporate latitude-saliency adaptive maps in the loss function to concentrate on important viewpoint regions with higher texture complexity and human-watching interest. In addition, we collect a new ODV-SR dataset with various scenarios. Extensive experimental results demonstrate that the proposed STDAN achieves superior super-resolution performance on ODVs and outperforms state-of-the-art methods.