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A combined theoretical and experimental study of thermodynamical, structural, and elastic properties of Fe3Al-based ternary alloys is presented. The theoretical part is based on a scale-bridging, multi-disciplinary combination of (i) thermodynamic aspects of the site preference and (ii) elastic stiffness data for substitutional ternary elements in Fe3Al single crystals, as determined by parameter-free first-principles calculations, and (iii) Hershey's homogenization model for the polycrystalline aggregates within the frame of linear elasticity theory. The approach was employed in order to explore the relation between chemical composition and both structural and elastic properties of Fe3Al ternary alloys containing the selected substituents (Ti, V, W, Cr and Si). The ab initio calculations employ density-functional theory (OFF) and the generalized gradient approximation (GGA). The determined elastic constants are used to calculate the elastic moduli, such as the Young's and bulk modulus. The theoretical results are compared to both literature data and novel impulse excitation measurements. Specifically, for Fe3Al-Ti alloys with low to medium Ti concentrations, an unexpected non-linear compositional dependence of the polycrystalline Young's modulus was found experimentally. The origin of this behavior is analyzed and discussed based on our theoretical results.