We investigate the elastic properties of the binary alloy Ag-Pd. The lattice constant of this system shows significant deviations from the linear behavior anticipated by the semi-empirical Vegard\'s rule. This effect was formerly studied by assuming total substitutional disorder, and described by the coherent potential approximation (CPA). Theoretical phase diagram investigations have however suggested three ordered phases at low temperatures, and we extend our first-principles investigation to include such scenarios through the adoption of an extended unit cell representation and a recently developed multisublattice generalization of the original CPA. This allows us to explore equilibrium lattice constant and bulk modulus within a unified approach even in the presence of partial long-range order. We obtain significant variations of the bulk modulus in comparison to the totally disordered picture, and again very rich deviations from more intuitive predictions of a simple linear behavior. We follow former suggestions to analyze the different regimes in connection with topological transitions of the Fermi surface, examined through Bloch spectral function calculations.