With the rapid growth of User-Generated Content (UGC) exchanged between users and sharing platforms, the need for video quality assessment in the wild is increasingly evident. UGC is typically acquired using consumer devices and undergoes multiple rounds of compression (transcoding) before reaching the end user. Therefore, traditional quality metrics that employ the original content as a reference are not suitable. In this paper, we propose ReLaX-VQA, a novel No-Reference Video Quality Assessment (NR-VQA) model that aims to address the challenges of evaluating the quality of diverse video content without reference to the original uncompressed videos. ReLaX-VQA uses frame differences to select spatio-temporal fragments intelligently together with different expressions of spatial features associated with the sampled frames. These are then used to better capture spatial and temporal variabilities in the quality of neighbouring frames. Furthermore, the model enhances abstraction by employing layer-stacking techniques in deep neural network features from Residual Networks and Vision Transformers. Extensive testing across four UGC datasets demonstrates that ReLaX-VQA consistently outperforms existing NR-VQA methods, achieving an average SRCC of 0.8658 and PLCC of 0.8873. Open-source code and trained models that will facilitate further research and applications of NR-VQA can be found at https://github.com/xinyiW915/ReLaX-VQA.