Reconstructing 3D MR volumes from multiple motion-corrupted stacks of 2D slices has shown promise in imaging of moving subjects, e. g., fetal MRI. However, existing slice-to-volume reconstruction methods are time-consuming, especially when a high-resolution volume is desired. Moreover, they are still vulnerable to severe subject motion and when image artifacts are present in acquired slices. In this work, we present NeSVoR, a resolution-agnostic slice-to-volume reconstruction method, which models the underlying volume as a continuous function of spatial coordinates with implicit neural representation. To improve robustness to subject motion and other image artifacts, we adopt a continuous and comprehensive slice acquisition model that takes into account rigid inter-slice motion, point spread function, and bias fields. NeSVoR also estimates pixel-wise and slice-wise variances of image noise and enables removal of outliers during reconstruction and visualization of uncertainty. Extensive experiments are performed on both simulated and in vivo data to evaluate the proposed method. Results show that NeSVoR achieves state-of-the-art reconstruction quality while providing two to ten-fold acceleration in reconstruction times over the state-of-the-art algorithms.