Traditional standalone embedded system is limited in their functionality, flexibility, and scalability. Fog computing platform, characterized by pushing the cloud services to the network edge, is a promising solution to support and strengthen traditional embedded system. Resource management is always a critical issue to the system performance. In this paper, we consider a fog computing supported software-defined embedded system, where task images lay in the storage server while computations can be conducted on either embedded device or a computation server. It is significant to design an efficient task scheduling and resource management strategy with minimized task completion time for promoting the user experience. To this end, three issues are investigated in this paper: 1) how to balance the workload on a client device and computation servers, i.e., task scheduling, 2) how to place task images on storage servers, i.e., resource management, and 3) how to balance the I/O interrupt requests among the storage servers. They are jointly considered and formulated as a mixed-integer nonlinear programming problem. To deal with its high computation complexity, a computation-efficient solution is proposed based on our formulation and validated by extensive simulation based studies.