Origami structures are often attractive for a broad range of applications in engineering, design, and robotics because of their useful characteristics such as reconfigurable geometry, tunable stiffness, and energy absorption capacity. Although a range of algorithms and software is available for origami design and folding analysis, they are generally isolated from other computational tools. To contribute to filling this research gap, we propose a unified parametric origami design workflow based on grasshopper combined with a multi-objective optimization process. To this end, first, a parametric model for a ring-shaped fourfold origami structure, called the Miura-oRing metastructure, is developed based on appropriate geometric parameters. Its nonlinear folding process is then simulated according to geometric compatibility conditions and given constraints. Simultaneously, modal analysis is iteratively performed, using SAP2000 through C# scripts, to obtain relationships for the structural configuration, mass, and stiffness of the origami structure. Finally, an inverse design process based on a fitting cylindrical annulus is carried out using Octopus, considering the spatial fit, mass, and stiffness of the Miura-oRing. A comparison is made between the obtained results and those of the origami simulator and the physical models to validate the performance of the proposed method. After balancing the three objectives of inverse design, a recommended range of parameters is prescribed for the Miura-oRing for a given set of dimensions. This study provides a workflow that integrates geometry, kinematics, and structural performance, enabling the design of origami structures with desirable geometric, kinematic, and structural characteristics.