Integrated sensing, communication, and computation (ISCC) has recently emerged as a unified framework for enabling edge intelligence. However, existing ISCC designs predominantly rely on single-modal sensing, which is inherently vulnerable to occlusions, environmental uncertainties, and modality-specific failures, leading to degraded robustness in real-world deployments. This motivates the need for multi-modal ISCC, yet its design remains insufficiently explored. Compared with the single-modal case, multi-modal ISCC is more challenging because heterogeneous modalities enlarge data dimensionality and tighten communication/computation/energy budgets, while inter-modal correlations further complicate performance characterization. To address these challenges, we propose a task-oriented multi-modal ISCC framework that integrates device-side feature extraction with edge-side joint multi-modal inference. A central component of our approach is the maximal coding rate reduction (MCR^2) criterion, which enables each device to learn compact and discriminative task-relevant features, offering clear advantages over conventional cross-entropy-based extractors. We further leverage MCR^2 as a principled metric for edge-side sensing evaluation. On this basis, we formulate a sensing accuracy maximization problem under delay and resource constraints and develop an efficient block coordinate descent (BCD) algorithm after transforming the problem into a more tractable equivalent form. Focusing on a human activity recognition task, we conduct extensive experiments on publicly available datasets to evaluate the performance of the proposed ISCC framework. The results demonstrate that our approach consistently outperforms three baseline schemes under limited resource conditions.