Bent-shaped molecules based oil the oxadiazole central core with various side wings and terminal chain groups have been synthesized, and their liquid-crystalline behavior was investigated by optical microscopic, X-ray, and electrooptic measurements. These molecules exhibit liquid-crystal polymorphism including both the calamitic and banana phases. Such a characteristic polymorphism is attributable to the larger bend angle of the oxadiazole core compared to that of the resorcinol core used in conventional banana molecules. Only one type of banana phase, designated as the Bx phase, is formed. It appears upon cooling from the nematic and smectic liquid crystals and exhibits chiral domains with a very weak birefringence (apparently optically isotropic). By applying an electric field, the Bx phase is altered to a high-birefringence B2 phase with a homochiral SMCAPA structure that exhibits in antiferroelectric response. From detailed analyses of the optical texture and X-ray patterns through the transformation from well-oriented calamitic phases, the Bx phase was found to exhibit a helical structure, which arises as a frustration from the ground-state B2 phase in such a manner that the blocks of B2 layers are twisted with respect to each other in a direction parallel to the layer plane similarly to the twisted grain boundary (TGB) phase.