This study investigates the efficacy of two dimensional (2D) carbon and inorganic nanostructures as reinforcing agents of crosslinked composites of the biodegradable and biocompatible polymer polypropylene fumarate (PPF) as a function of nanostructure concentration. PPF composites were reinforced using various 2D nanostructures: single- and multi-walled graphene oxide nanoribbons (SWGONRs, MWGONRs), graphene oxide nanoplatelets (GONPs), and molybdenum di-sulfite nanoplatelets (MSNPs) at 0.01–0.2 weight% concentrations. Cross-linked PPF was used as the baseline control, and PPF composites reinforced with single- or multi-walled carbon nanotubes (SWCNT, MWCNT) were used as positive controls. Compression and flexural testing show a significant enhancement (i.e., compressive modulus = 35–108%, compressive yield strength = 26–93%, flexural modulus = 15–53%, and flexural yield strength = 101–262% greater than the baseline control) in the mechanical properties of the 2D-reinforced PPF nanocomposites. MSNPs nanocomposites consistently showed the highest values among the experimental or control groups in all the mechanical measurements. In general, the inorganic nanoparticle MSNPs showed a better or equivalent mechanical reinforcement compared to carbon nanomaterials, and 2-D nanostructures (GONP, MSNP) are better reinforcing agents compared to 1-D nanostructures (e.g. SWCNTs). The results also indicate that the extent of mechanical reinforcement is closely dependent on the nanostructure morphology and follows the trend nanoplatelets > nanoribbons > nanotubes. Transmission electron microscopy of the cross-linked nanocomposites indicates good dispersion of nanomaterials in the polymer matrix without the use of a surfactant. The sol-fraction analysis showed significant changes in the polymer cross-linking in the presence of MSNP (0.01–0.2 wt %) and higher loading concentrations of GONP and MWGONR (0.1–0.2 wt%). The analysis of surface area and aspect ratio of the nanostructures taken together with the above results indicates differences in nanostructure architecture (2D vs. 1D nanostructures), as well as the chemical compositions (inorganic vs. carbon nanostructures), number of functional groups, and structural defects for the 2D nanostructures maybe key properties that affect the mechanical properties of 2D nanostructure-reinforced PPF nanocomposites, and the reason for the enhanced mechanical properties compared to the controls.