We study source characteristics of the September 28, 2017 M-w 7.5 Palu (Sulawesi, Indonesia) earthquake that occurred in central Sulawesi and triggered devastating tsunami waves along the coastal plains of the island. We apply point-source teleseismic P-and SH-body waveform inversion and kinematic slip inversion techniques to obtain double-couple source mechanism and comprehensive finite-fault slip model of the source. The overall results show a strike-slip faulting mechanism (strike: 353 degrees +/- 5 degrees, dip: 65 degrees +/- 5 degrees and rake angles: -4 degrees +/- 5 degrees) with a small amount of dip-slip component at a shallow focal depth of 16 +/- 2 km associated with the NW-SE trending left-lateral Palu-Koro strike-slip fault in the central Sulawesi region. The P-wave first motion polarity readings recorded at near-field and regional seismic stations are found to be reasonably consistent with the source mechanism solution of the earthquake and estimated error limits. We have extensively studied and considered the rupture velocity to be about 4.1 km/s during the slip inversion as previously proposed by seismological and geodetic studies for this event. The obtained finite-fault slip distribution model displays a rupture starting from the hypocentre located at 16 km, and then it propagated south accompanied by high amount of displacement, and reached the surface. The model has two slip-patches of 2.0-4.0 m at north of the fault plane, and 5.0-6.3 m at south near Palu city, which is very well matched with the observed damage and destruction related to the earthquake. The fault length and width, average slip and stress drop values are estimated to be 150 km, 45 km, 1.5 m and 13 bars, respectively. We have also obtained total source duration to be about 40 s with the most of seismic energy released at 10 s and 25 s. Furthermore, a small dip-slip component is evidently observed from both source models, and we suggest that this oblique shear which reflects the bending of slip vector along the strike direction could be comparatively responsible for tsunami generation along the left-lateral Palu-Koro Fault. The validation of this hypothesis could be done by evaluating the results of the mathematical tsunami simulations based on the comprehensive non-uniform slip models along with a high-resolution bathymetry data, which provides the details of the continental shelf in Palu bay.