Based on density functional theory (DFT), the formation energies of intrinsic vacancy defects (V_C, V_Si, and V_Si+C) and oxygen-related defects (O_C, O_Si, O_CV_Si, and O_SiV_C) in 3C-SiC are calculated. The results indicate that all defects considered, except for O_C, possess neutral or negative charge states, thereby making them suitable for detection by positron annihilation spectroscopy (PAS). Furthermore, the electron and positron density distributions and positron annihilation lifetimes for the perfect 3C-SiC supercell and various defective configurations are computed. It is found that the O_Si and O_SiV_C complexes act as effective positron trapping centers, leading to the formation of positron trapped states and a notable increase in annihilation lifetimes at the corresponding defect sites. In addition, coincidence Doppler broadening (CDB) spectra, along with the S and W parameters, are calculated for both intrinsic and oxygen-doped point defects (O_C, O_Si, O_CV_Si, and O_SiV_C). The analysis reveals that electron screening effects dominate the annihilation characteristics of the O_Si defect, whereas positron localization induced by the vacancy is the predominant contributor in the case of O_SiV_C. This distinction results in clearly different momentum distributions of these two oxygen-related defects for different charge states. Overall, the PAS is demonstrated to be a powerful technique for distinguishing intrinsic vacancy-type defects and oxygen-doped composites in 3C-SiC. Combining the analysis of electron and positron density distributions, the electron localization and positron trapping behavior in defect systems with different charge states can be comprehensively understood. These first-principles results provide a solid theoretical foundation for identifying and characterizing the defects in oxygen-doped 3C-SiC by using positron annihilation spectroscopy.