SodsMPC is a quantum-safe smart contract system. SodsMPC permissioned servers (verification nodes) execute contracts by secure multi-party computation (MPC) protocols. MPC ensures the contract execution correctness while trivially keeping the data privacy. Moreover, SodsMPC accomplishes the contract business logic privacy while protecting the contract user anonymous identity simultaneously. We express the logic of a contract by a finite state machine (FSM). A state transition of the FSM is represented by a blind polynomial with secret-shared coefficients. When using MPC to compute this blind polynomial, the contract business logic privacy is obtained. These coefficients which control the logic are binary secret shares. We also propose a base conversion method among binary and integer secret shares by MPC. Our contract anonymity comes from the 'mixing-then-contract' paradigm. The online phase of the SodsMPC mixing is a multiplication between a preprocessed permutation matrix and an input vector in the form of secret sharing, which accomplishes a fully randomized shuffle of the inputs and keeps the secret share form for the following contract execution. All SodsMPC components, including a verifiable secret sharing scheme, are quantum-safe, asynchronous, coping with t < n/3 compromised servers, and robust (tolerates Byzantine servers) in both preprocessing and online phases.