As origami structures display designable and predictable folding or unfolding shape changes, the origami-inspired mechanical metamaterials have recently been extensively investigated for applications in metamaterial engineering. There were many previous studies on the conventional hexagonal Kresling origami structures, however, there are still many issues such as structural optimizations and designable strategies for the mechanical metamaterials. To solve these issues, in this study, we investigated the influences of crease direction, number of sides, and unit arrangement on the origami structures. Effects of these parameters on mechanical properties and deformation behaviors of metamaterials were analyzed using finite element method and experimental verifications. Effects of continuous changes in the number of sides were investigated, and we found that the switching of the metamaterials from a monostable state at number of sides of 3 to a quasi-static stiffness one at 4, and then to bistable ones at 5, 6, 7 and 8 can be realized. The compression–twist coupling effects of these metamaterials can be adjustable and tailorable by arranging the chosen units in series. These designed foldable metamaterials are flexible, especially in their unfolding and folding directions, resulting in the achievement of unstable compression states, i.e. the externally applied loads may cause the structure to unfold along the same compression path. Furthermore, shape memory polymer has been printed using 3D printing technology to achieve the smart origami metamaterials, which endow the metamaterials with shape memory effect, self-adaptability and temperature-responsive mechanical behavior.