Image deblurring has seen a great improvement with the development of deep neural networks. In practice, however, blurry images often suffer from additional degradations such as downscaling and compression. To address these challenges, we propose an Enhanced Deep Pyramid Network (EDPN) for blurry image restoration from multiple degradations, by fully exploiting the self- and cross-scale similarities in the degraded image.Specifically, we design two pyramid-based modules, i.e., the pyramid progressive transfer (PPT) module and the pyramid self-attention (PSA) module, as the main components of the proposed network. By taking several replicated blurry images as inputs, the PPT module transfers both self- and cross-scale similarity information from the same degraded image in a progressive manner. Then, the PSA module fuses the above transferred features for subsequent restoration using self- and spatial-attention mechanisms. Experimental results demonstrate that our method significantly outperforms existing solutions for blurry image super-resolution and blurry image deblocking. In the NTIRE 2021 Image Deblurring Challenge, EDPN achieves the best PSNR/SSIM/LPIPS scores in Track 1 (Low Resolution) and the best SSIM/LPIPS scores in Track 2 (JPEG Artifacts).