Higher-order polygonal finite elements are developed for adaptive analyses of linear elastic problem. These elements are constructed using virtual node method based on partition of unity coupled with polynomial enrichment functions. Because the element shape functions are polynomials, the stiffness matrix is computed precisely with standard Gauss quadrature rules. Several numerical examples of linear elasticity are presented to validate the accuracy and convergence of the proposed elements. One of the advantages of the proposed elements is that they can be used as transition elements with hanging nodes on higher-order approximation meshes. Building on this advantage, h- and hp-adaptive finite element analyses of numerical examples with local singularities are performed on triangular quadtree meshes in order to demonstrate the performance of the adaptive strategies using the proposed elements.