As the application of neural radiance fields (NeRFs) in various 3D vision tasks continues to expand, numerous NeRF-based style transfer techniques have been developed. However, existing methods typically integrate style statistics into the original NeRF pipeline, often leading to suboptimal results in both content preservation and artistic stylization. In this paper, we present multi-level dynamic style transfer for NeRFs (MDS-NeRF), a novel approach that reengineers the NeRF pipeline specifically for stylization and incorporates an innovative dynamic style injection module. Particularly, we propose a multi-level feature adaptor that helps generate a multi-level feature grid representation from the content radiance field, effectively capturing the multi-scale spatial structure of the scene. In addition, we present a dynamic style injection module that learns to extract relevant style features and adaptively integrates them into the content patterns. The stylized multi-level features are then transformed into the final stylized view through our proposed multi-level cascade decoder. Furthermore, we extend our 3D style transfer method to support omni-view style transfer using 3D style references. Extensive experiments demonstrate that MDS-NeRF achieves outstanding performance for 3D style transfer, preserving multi-scale spatial structures while effectively transferring stylistic characteristics.