We show spin-transfer-torque-driven vortex oscillations in current-perpendicular-to-plane giant magnetoresistance junctions using epitaxially grown Co2FexMn1-xSi (CFMS) Heusler alloy thin films. The soft magnetic property and high spin polarization of CFMS enable us to realize vortex oscillation emitting large microwave power with a low threshold current. The output power is maximized for a certain Fe-Mn composition ratio associated with a reduction of the threshold current for the oscillation, which is in agreement with a general model for spin-torque oscillation. Through comparison with an analytical theory that describes the translational motion of a vortex core, we show that the vortex core motion excited in the present device is inhomogeneous along the thickness direction. In spite of the inhomogeneity, the gyration radius at the CFMS/spacer interface region was estimated to be ∼75% of the actual ferromagnetic layer radius, which indicates that the CFMS-based all-metallic junction is useful for achieving large-amplitude vortex core motion. This comprehensive investigation would also be useful for designing high-performance all-metallic nano-oscillators based on magnetic vortex dynamics.