It is well known that the Strategic Petroleum Reserve in salt caverns is an important means to solve the potential petroleum shortage. However, salt mines in China are mainly lacustrine-layered structures with many mudstone interlayers. Meanwhile, the acid value of extracted crude oil has been increasing in recent years. The acid erosion of salt cavern interlayers by crude oil would affect the safety of bedded salt cavern oil storage. Therefore, combined with acoustic emission technology, the multistage creep mechanical behaviors of natural mudstone interlayer samples and the mudstone interlayer samples treated by oil erosion are studied in this paper. The internal structures of interlayer samples before and after oil erosion were systematically analyzed by SEM. The results show that petroleum acid (naphthenic acid) plays a significant deterioration role in the mechanical properties of mudstone interlayers during the petroleum reserve process. Compared with the uncorroded samples, the mudstone interlayers after oil erosion show obvious brittle failure characteristics. At low stress levels, the axial strain grows stepwise and the lateral strain is smaller than the axial strain. At high stress levels, however, the lateral creep is obviously higher than the axial creep. A large number of AE signals were generated at the initial loading stage for different stress levels. After the creep stabilized, the AE signals were significantly reduced. During the process of petroleum erosion, the internal pores in rocks continued to develop with the dissolution of many mineral particles. This suggests that crude oil storage in the bedded salt rocks could accelerate the deterioration of the surrounding rocks via erosion. This paper could provide basic research data and a reference for the construction of oil storage in the bedded salt rocks.