A clear understanding of the mechanical behavior of nanometer thick films on nanostructures, as well as developing versatile approaches to characterize their mechanical properties, are of great importance and may serve as the foundation for understanding and controlling molecular interactions at the interface of nanostructures. Here we report on the synthesis of thin, compressible polyethylene glycol (PEG) monolayers with a wet thickness of <20 nm on tin dioxide (SnO2) nanofibers through silane-based chemistries. Nanomechanical properties of such thin PEG films were extensively investigated using atomic force microscopy (AFM). In addition, tip-sample interactions were carefully studied, with different AFM tip modifications (i.e., hydrophilic and hydrophobic) and in different ionic solutions. We find that the steric forces dominate the tip-sample interactions when the polymer film is immersed in solution with salt concentrations similar to biological media (e.g., 1x phosphate buffer solution), while van der Waals and electrostatic forces have minimal contributions. A Dimitriadis thin film polymer compression model shows that the linear elastic regime is reproducible in the initial 50% indentation of these films which have tunable Young's moduli ranging from 5 MPa for the low molecular weight films to 700 kPa for the high molecular weight PEG films. Results are compared with the same PEG films deposited on silicon substrates which helped quantify the structural properties and understand the relationship between the structural and the mechanical properties of PEG films on the SnO2 fibers.