We here present the results from a detailed analysis of nebular abundances of commonly observed ions in the collisional ring galaxy Cartwheel using the Very Large Telescope (VLT) Multi-Unit Spectroscopic Explorer (MUSE) dataset. The analysis includes 221 HII regions in the star-forming ring, in addition to 40 relatively fainter Ha-emitting regions in the spokes, disk and the inner ring. The ionic abundances of He, N, O and Fe are obtained using the direct method (DM) for 9, 20, 20, and 17 ring HII regions, respectively, where the S++ temperature-sensitive line is detected. For the rest of the regions, including all the nebulae between the inner and the outer ring, we obtained O abundances using the strong-line method (SLM). The ring regions have a median 12+log(O/H)=8.19+/-0.15, log(N/O)=-1.57+/-0.09 and log(Fe/O)=-2.24+/-0.09 using the DM. Within the range of O abundances seen in the Cartwheel, the N/O and Fe/O values decrease proportionately with increasing O, suggesting local enrichment of O without corresponding enrichment of primary N and Fe. The O abundances of the disk HII regions obtained using the SLM show a well-defined radial gradient. The mean O abundance of the ring HII regions is lower by ~0.1dex as compared to the extrapolation of the radial gradient. The observed trends suggest the preservation of the pre-collisional abundance gradient, displacement of most of the processed elements to the ring, as predicted by the recent simulation by Renaud et al. (2018MNRAS.473..585R), and post- collisional infall of metal-poor gas in the ring.