The fabrication of core-shell structures is crucial for many nanowire device concepts. For the proper tailoring of their electronic properties, control of structural parameters such as shape, size, diameter of core and shell, their chemical composition, and information on their strain fields is mandatory. Using synchrotron X-ray diffraction studies and finite element simulations, we determined the chemical composition, dimensions, and strain distribution for series of InAs/InAsP core-shell wires grown on Si(111) with systematically varied growth parameters. In particular we detect initiation of plastic relaxation of these structures with increasing shell thickness and/or increasing phosphorus content. We establish a phase diagram, defining the region of parameters leading to pseudomorphic nanowire growth. This is important to avoid extended defects which are detrimental for their electronic properties.