As a paradigm shift towards pervasive intelligence, semantic communication (SemCom) has shown great potentials to improve communication efficiency and provide user-centric services by delivering task-oriented semantic meanings. However, the exponential growth in connected devices, data volumes, and communication demands presents significant challenges for practical SemCom design, particularly in resource-constrained wireless networks. In this work, we first propose a task-agnostic SemCom (TASC) framework that can handle diverse tasks with multiple modalities. Aiming to explore the interplay between communications and intelligent tasks from the information-theoretical perspective, we leverage information bottleneck (IB) theory and propose a distributed multimodal IB (DMIB) principle to learn minimal and sufficient unimodal and multimodal information effectively by discarding redundancy while preserving task-related information. To further reduce the communication overhead, we develop an adaptive semantic feature transmission method under dynamic channel conditions. Then, TASC is trained based on federated meta-learning (FML) for rapid adaptation and generalization in wireless networks. To gain deep insights, we rigorously conduct theoretical analysis and devise resource management to accelerate convergence while minimizing the training latency and energy consumption. Moreover, we develop a joint user selection and resource allocation algorithm to address the non-convex problem with theoretical guarantees. Extensive simulation results validate the effectiveness and superiority of the proposed TASC compared to baselines.