In this study, an attempt has been made to find out the possibility of extending the conventional engineering applications of Maleic Anhydride–grafted Polyethylene (MA-g-PE), compatibilized Ethylene-co-Vinyl Acetate (EVA), and High-Density Polyethylene (HDPE) polymer blends with the addition of Organo-Modified Montmorillonite (OMMT) nanoclay to sliding wear–resistant parts in the automobile, aerospace, and other similar industries. An experimental analysis of dry sliding friction and wear has been investigated for MA-g-PE (2 parts per hundred, i.e., phr) grafted EVA/HDPE (70/30 by weight %) blend with the addition of 0, 1, 2, 3, and 4 phr of OMMT nanoclay. According to ASTM G99, Standard Test Method for Wear Testing with a Pin-on-Disk Apparatus, specimens slid against an EN31 steel disk of 60 HRC using a wear and friction tribometer at different forces, sliding distances, and sliding velocities. Effects of forces and sliding distances on sliding friction coefficients and specific wear rates of polymer nanocomposites were evaluated. It was observed that the coefficient of friction decreased with the increase in forces and slightly varied with increments in sliding distance. On the other hand, the specific wear rate increased by increment in forces and decreased with the increase in sliding distance. Wear mechanisms and worn surfaces were analyzed using scanning electron microscopic images. Parametric study of influencing factors (polymer compositions, forces, sliding distances, and sliding velocities) was conducted using the Taguchi design of experiment and ANalysis Of VAriance (ANOVA). Taguchi was used to rank and optimize four influencing factors, viz., composition, force, sliding distance, and sliding velocity. ANOVA determined the statistical significance and percentage contribution of control factors.