Data privacy is becoming one of the most critical concerns in cloud computing. Several proposals based on Intel SGX such as VC3 [1] and M2R [2] have been introduced in the literature to protect data privacy during job execution in the cloud. However, a comprehensive formal proof of their security guarantees is still lacking. In this paper, we propose ObliDC, a general UC-secure SGX-based oblivious distributed computing framework. First, we model the life-cycle of a distributed computing job as data-flow graphs. Under the assumption of malicious, adaptive adversaries in the cloud, we then formally define data privacy of a distributed computing job by introducing a notion named ODC-privacy, which encompasses both semantic security (to protect data confidentiality during computation and transmission) and oblivious traffic (to prevent data leakage from traffic analysis). ObliDC is composed of four two-party protocols -- job deployment, job initialization, job execution, and results return, which allow for modular construction of concrete privacy-preserving job protocols in different distributed computing frameworks. Finally, inspired by a formal abstraction for trusted processors proposed by R. Pass et al. [3], we formally prove the security of ObliDC under the universal composability (UC) framework.