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 many issues such as structural optimizations and designable strategies for the mechanical metamaterials, which have not been solved. To solve these issues, in this study, we studied the influences of crease direction, the 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 methods and experimental verifications. By adjusting the number of sides, the switching between monostability and bistability of the metamaterials was realized. The compression-twist coupling effect of these metamaterials can be adjustable and tailorable by arranging the chosen units in series. Designed foldable metamaterials are flexible, especially in their unfolding and folding directions, resulting in the achievement of an unstable compression state, i.e., the externally applied loads may cause the structure to unfold along the same compression path. Furthermore, shape memory polymer (SMP) 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.