We report on experimental determination of the strain and bandgap of InAsP in epitaxially grown InAsP-InP core-shell nanowires. The core-shell nanowires are grown via metal-organic vapor phase epitaxy. The as-grown nanowires are characterized by transmission electron microscopy, X-ray diffraction, micro-photoluminescence (mu PL) spectroscopy, and micro-Raman (mu-Raman) spectroscopy measurements. We observe that the core-shell nanowires are of wurtzite (WZ) crystal phase and are coherently strained with the core and the shell having the same number of atomic planes in each nanowire. We determine the predominantly uniaxial strains formed in the core-shell nanowires along the nanowire growth axis and demonstrate that the strains can be described using an analytical expression. The bandgap energies in the strained WZ InAsP core materials are extracted from the mu PL measurements of individual core-shell nanowires. The coherently strained core-shell nanowires demonstrated in this work offer the potentials for use in constructing novel optoelectronic devices and for development of piezoelectric photovoltaic devices.