Spiking Neural Networks (SNNs) offer an energy-efficient paradigm for machine intelligence, but their continued scaling poses challenges for resource-limited deployment. Despite recent advances in binary SNNs, the storage and computational demands remain substantial for large-scale networks. To further explore the compression and acceleration potential of SNNs, we propose Sub-bit Spiking Neural Networks (S$^2$NNs) that represent weights with less than one bit. Specifically, we first establish an S$^2$NN baseline by leveraging the clustering patterns of kernels in well-trained binary SNNs. This baseline is highly efficient but suffers from \textit{outlier-induced codeword selection bias} during training. To mitigate this issue, we propose an \textit{outlier-aware sub-bit weight quantization} (OS-Quant) method, which optimizes codeword selection by identifying and adaptively scaling outliers. Furthermore, we propose a \textit{membrane potential-based feature distillation} (MPFD) method, improving the performance of highly compressed S$^2$NN via more precise guidance from a teacher model. Extensive results on vision reveal that S$^2$NN outperforms existing quantized SNNs in both performance and efficiency, making it promising for edge computing applications.