Automatic sleep stage scoring is crucial for the diagnosis and treatment of sleep disorders. Although deep learning models have advanced the field, many existing models are computationally demanding and designed for single-channel electroencephalography (EEG), limiting their practicality for multimodal polysomnography (PSG) data. To overcome this, we propose ULW-SleepNet, an ultra-lightweight multimodal sleep stage scoring framework that efficiently integrates information from multiple physiological signals. ULW-SleepNet incorporates a novel Dual-Stream Separable Convolution (DSSC) Block, depthwise separable convolutions, channel-wise parameter sharing, and global average pooling to reduce computational overhead while maintaining competitive accuracy. Evaluated on the Sleep-EDF-20 and Sleep-EDF-78 datasets, ULW-SleepNet achieves accuracies of 86.9% and 81.4%, respectively, with only 13.3K parameters and 7.89M FLOPs. Compared to state-of-the-art methods, our model reduces parameters by up to 98.6% with only marginal performance loss, demonstrating its strong potential for real-time sleep monitoring on wearable and IoT devices. The source code for this study is publicly available at https://github.com/wzw999/ULW-SLEEPNET.