Orthogonal minimally aliased response surface (OMARS) designs have orthogonal main effects and no aliasing between main effects and second-order effects, making them suitable for both factor screening and response surface modeling. However, OMARS designs with the same parameters may exhibit different projection and aliasing properties. We propose generalized aberration criteria based on three- and four-factor projections. A new J_4^*-characteristic measures the aliasing between quadratic effects and two-factor interactions, complementing the conventional J_4-characteristic for aliasing among two-factor interactions. The resulting criteria apply to both three-level and mixed-level OMARS designs, providing a systematic basis for design selection. We also present Paley-based algebraic constructions of three-level OMARS designs with desirable second-order properties. The constructed designs inherit favorable projection properties from the Paley construction. We characterize these properties and use the generalized aberration criteria to identify promising designs. These results provide practical guidance for experimenters in constructing and selecting appropriate OMARS designs.