Eight new open-framework inorganic-organic hybrid compounds based on indium have been synthesized employing hydrothermal methods. All of the compounds have InO6, C2O4, and HPO3/HPO4/SO4 units connected to form structures of different dimensionality Thus, the compounds have zero-(I), two- (II, III, IV, V, VII, and VIII), and three-dimensionally (VI) extended networks. The formation of the first zero-dimensional hybrid compound is noteworthy In addition, concomitant polymorphic structures have been observed in the present study. The molecular compound, I, was found to be reactive, and the transformation studies in the presence of a base (pyridine) give rise to the polymorphic structures of II and III, while the addition of an acid (H3PO3) gives rise to a new indium phosphite with a pillared layer structure (T1). Preliminary density functional theory calculations suggest that the stabilities of the polymorphs are different, with one of the forms (II) being preferred over the other, which is consistent with the observed experimental behavior. The oxalate units perform more than one role in the present structures. Thus, the oxalate units connect two In centers to satisfy the coordination requirements as well as to achieve charge balance in compounds II, IV, and VI. The terminal oxalate units observed in compounds I, IV, and V suggest the possibility of intermediate structures. Both in-plane and out-of-plane connectivity of the oxalate units were observed in compound VI. The 31 compounds have been characterized by powder X-ray diffraction, IR spectroscopy, thermogravimetric analysis, and P-31 NMR studies.