Multi-principal element alloys (MPEAs), also known as high-entropy alloys (HEAs), are novel materials that have received significant attention due to their exceptional mechanical properties, thermal stability, and resistance to wear and corrosion. These alloys are typically composed of multiple principal elements in near-equal atomic proportions, forming solid solution phases such as face-centered cubic (FCC) or body-centered cubic (BCC) structures. Despite the promising applications, a more in-depth understanding of the atomic-level behavior, particularly, lattice distortion and atomic strain, is essential to better design and optimize these materials in extreme environments. This study focuses on systematically investigating the atomic-scale lattice distortion characteristics and their influence on atomic strain in three representative BCC-based MPEAs: TaWNbMo, TiZrNb, and CoFeNiTi. We utilize molecular dynamics (MD) simulations to explore the local atomic strain distributions in these alloys at various temperatures. Von Mises strain and volumetric strain are employed as key descriptors to quantify the atomic strain, providing a clear representation of how lattice distortion on an atomic scale influences the overall strain behavior. The study specifically addresses the effects of atomic radius differences, chemical short-range ordering, and temperature on the strain characteristics of the alloys. The results obtained indicate that an increase in lattice distortion corresponds to a broader distribution of von Mises strain and volumetric strain, with strain values significantly amplified. More precisely, alloys with larger atomic radius differences exhibit greater volumetric strain, reflecting the influence of atomic size disparity on strain distribution. Furthermore, the formation of chemical short-range order (CSRO) significantly mitigates lattice distortion and atomic strain. This finding highlights the importance of short-range atomic ordering in enhancing the stability of the alloy structures, thus potentially improving their mechanical properties. Temperature effects are also investigated, revealing that elevated temperature induces more intense atomic vibration, which in turn increases the atomic strain. The findings underscore the complex interplay between atomic-scale phenomena and macroscopic mechanical properties, offering new insights into the microscopic mechanical behavior of high-entropy alloys. This study contributes to a better understanding of the underlying mechanisms driving atomic strain and lattice distortion in MPEAs. The results provide valuable theoretical insights that can guide the design of high-performance alloys tailored for high-temperature and extreme environments. By addressing the key factors influencing atomic strain, such as atomic radius, chemical ordering, and temperature, this work lays the foundation for future research aimed at enhancing the mechanical performance of MPEAs in various industrial applications.