Shale oil is mainly stored in the nano–micro-pores of shale in the form of adsorption or in a free state. Among them, only free-state oil is the main contributor to shale oil production under natural elastic energy. Therefore, it is crucial to evaluate the movability of crude oil effectively. In this paper, focusing on the Jurassic shale oil reservoir core in the middle-eastern Sichuan region of China, low-field nuclear magnetic resonance (NMR) technology is used to analyze the basic characteristics of shale oil core samples. Experiments on the low-field NMR one-dimensional and two-dimensional spectrum characteristics of the original core, heat-treated core, and thermogravimetric-treated shale core are carried out. The effects of the TG-MS method, T2 method, and the volatilization of light oil components on the movability of shale oil reservoirs are analyzed, and the movability characteristics of shale oil reservoirs in the middle-eastern Sichuan region are preliminarily clarified. The results show that under thermal treatment, the distribution range of the two-dimensional spectrum of the core oil occurrence area is significantly reduced, and the T1 and T2 distribution ranges are reduced by 10.9% and 60.7%, respectively. According to the TG-MS method, the mobile oil, bound oil, and adsorbed oil account for 74.7%, 8.1%, and 17.2%, respectively. The quantitative calculation of movable oil saturation by NMR combined with heat treatment is 65.6%, which is lower than that calculated using the thermogravimetric method. In order to calculate the movability more accurately, the scale effect between different samples should be considered. This study could provide a theoretical basis for the subsequent shale oil development program.