Industrial anomaly detection has attracted significant attention as a fundamental challenge in industrial systems. The rapid advancement of heterogeneous industrial sensors has driven industrial anomaly detection from unimodal to multimodal paradigms. However, existing methods are primarily designed for centralized and offline settings, overlooking the distributed and continuously generated data characteristic of real-world industrial environments. With the advancement of edge intelligence, modern edge devices are increasingly capable of not only data acquisition but also distributed model training, enabling collaborative intelligence across the system. Industrial anomaly detection represents a critical application in this context. Motivated by these challenges, we propose a novel framework termed Multimodal Online Distributed Industrial Anomaly Detection (MODIAD). We first present a comprehensive workflow for MODIAD and then formulate a Multi-class Intelligent Scheduling (MIS) problem to coordinate cross class model updates by balancing data sufficiency and class update frequency. To efficiently solve this problem, we design a Sequential Marginal Gain Greedy (SMG) algorithm that enables effective multi-class training under resource constraints. Furthermore, to improve the computational and communication efficiency during training, we propose an Resource Efficient Class-Wise Low Rank Adaptation (REC-LoRA) strategy, which significantly reduces system overhead while preserving detection performance. Extensive experiments on two representative multimodal industrial anomaly detection datasets, MVTec 3D-AD and Eyecandies demonstrate that the proposed approach achieves superior performance and efficiency under the MODIAD scenario.