A symmetry analysis and a semianalytical exact model are proposed to describe the mechanical, piezoelectric, and electronic properties of strained wurtzite quantum nanostructures with axial symmetry. An expression of the piezoelectric polarization is given as a function of inhomogeneous strains. The three-dimensional 8x8 strained kp Hamiltonian is reduced to two-dimensional using the total angular momentum representation. When the spin-orbit coupling is neglected, the Hamiltonians are reduced to 1x1 and 3x3 Hamiltonians for the states in the S-shell. For all the other shells, the fourfold degeneracy is demonstrated. Simulations are performed for InN/GaN quantum dots.