Mismatched epitaxial layers of InxGa1-xAs and InyAl1-yAs were grown on InP by molecular beam epitaxy. Samples were characterized by high-resolution x-ray diffraction to assess layer quality as well as composition and strain. Measurement of epitaxial layer peak width is shown to be a sensitive, nondestructive means to judge the structural quality of a strained heterostructure. We find that for lattice mismatch of +/- 1 % or less, the crystalline quality of epitaxial layers of InGaAs and InAlAs consistently remains high to thicknesses up to 3-9 times the Matthews-Blakeslee [J. Cryst. Growth 27, 118 (1974)] critical layer thickness. The findings are applied to the design and growth of high-performance mismatched InAlAs/InGaAs/InP heterostructure field-effect transistors.