Real-time multimodal inference on resource-constrained edge devices is essential for applications such as autonomous driving, human-computer interaction, and mobile health. However, prior work often overlooks the tight coupling between sensing dynamics and model execution, as well as the complex inter-modality dependencies. In this paper, we propose MMEdge, a new on-device multimodal inference framework based on pipelined sensing and encoding. Instead of waiting for complete sensor inputs, MMEdge decomposes the entire inference process into a sequence of fine-grained sensing and encoding units, allowing computation to proceed incrementally as data arrive. MMEdge also introduces a lightweight but effective temporal aggregation module that captures rich temporal dynamics across different pipelined units to maintain accuracy performance. Such pipelined design also opens up opportunities for fine-grained cross-modal optimization and early decision-making during inference. To further enhance system performance under resource variability and input data complexity, MMEdge incorporates an adaptive multimodal configuration optimizer that dynamically selects optimal sensing and model configurations for each modality under latency constraints, and a cross-modal speculative skipping mechanism that bypasses future units of slower modalities when early predictions reach sufficient confidence. We evaluate MMEdge using two public multimodal datasets and deploy it on a real-world unmanned aerial vehicle (UAV)-based multimodal testbed. The results show that MMEdge significantly reduces end-to-end latency while maintaining high task accuracy across various system and data dynamics. A video demonstration of MMEdge’s performance in real world is available at https://youtu.be/qRew7sT-iWw.