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We address the carrier concentration, strain, and bandgap issue of InN films grown on c-sapphire at different N-flux by molecular beam epitaxy using x-ray diffraction and x-ray photoelectron spectroscopy. We demonstrate that the strain in InN films arises due to point defects like nitrogen interstitials and nitrogen antisites. We report minimal biaxial strain due to relaxed growth morphology and a minimal hydrostatic strain arising due to interstitial nitrogen atoms being partially compensated by nitrogen antisites. We find that the variation in absorption edge can be attributed to defect induced carrier concentration and that nitrogen interstitials and nitrogen antisites act as donors that yield the respective absorption edge and Moss-Burstein shift. Our studies are a step towards the ability to form low carrier concentration strain-relaxed films and to determine the intrinsic band gap value for this technologically important material.