Stiffness usually increases with the lattice-distortion-induced strain, as observed in many nanostructures. Partly due to the size differences in the component elements, severe lattice distortion naturally exists in high entropy alloys (HEAs). The single-phase face-centered-cubic (FCC) Al0.3CoCrFeNi HEA, which has large size differences among its constituent elements, is an ideal system to study the relationship between the elastic properties and lattice distortion using a combined experimental and computational approach based on in-situ neutron-diffraction (ND) characterizations, and first-principles calculations. Analysis of the interatomic distance distributions from calculations of optimized special quasi random structure (SQS) found that the HEA has a high degree of lattice distortion. When the lattice distortion is explicitly considered, elastic properties calculated using SQS are in excellent agreement with experimental measurements for the HEA. The calculated elastic constant values are within 5% of the ND measurements. A comparison of calculations from the optimized SQS and the SQS with ideal lattice sites indicate that the lattice distortion results in the reduced stiffness. The optimized SQS has a bulk modulus of 177 GPa compared to the ideal lattice SQS with a bulk modulus of 194 GPa. Machine learning (ML) modeling is also implemented to explore the use of fast, and computationally efficient models for predicting the elastic moduli of HEAs. ML models trained on a large dataset of inorganic structures are shown to make accurate predictions of elastic properties for the HEA. The ML models also demonstrate the dependence of bulk and shear moduli on several material features which can act as guides for tuning elastic properties in HEAs. Display omitted