Metamaterials play a prominent role among porous materials due to their highly controllable architectures and diverse effective properties. A novel class of metamaterial, composed of curved struts, is investigated. Unlike conventional designs that rely on straight struts as fundamental building blocks, the proposed curved-strut architecture provides a wider elastic stiffness range with enhanced geometric flexibility, expanding the application potential of strut-based metamaterials. To facilitate fast and direct design of curved strut metamaterial cells with prescribed effective properties, an edge-conditioned graph neural network (ECGNN) based inverse generator is developed. It benefits from the graph representation of strut-based architecture, using edges to represent struts connecting the nodes and encoding strut information as edge feature. The trained model achieves high accuracy in generating cell geometries that match target properties. The inverse generator is further integrated into a multiscale structural optimisation framework, specifically a topology optimisation (TO) based framework achieving target deformation profiles. This method determines the optimal property distribution via TO, followed by automatic generation and assembly of corresponding metamaterial cells. Numerical examples on deformation control demonstrate the effectiveness of the proposed method with profile agreement over 99%. One major contribution of this work is the use of an edge-conditioned graph representation to model strut-based metamaterials, encoding curved strut geometry as edge features for efficient learning, and its application to the design of architectured structures with prescribed deformation behaviour.