We present a derivation of the 6× 6 valence band Hamiltonian valid for general [h 0 il] oriented III-V wurtzite strained substrates. The derivation is performed within the exact envelope function theory approach in which the k̂ operators are written in an ordered form when the Hamiltonian is applied to wurtzite superlattices. The choice of suitable basis functions for the (h 0 il) growth direction, written in terms of those for the typical (0001) case, allows us to define the heavy-, light-, and split-off-hole states in a transparent way and without ambiguities. The Hamiltonian for the (101 0) oriented crystals is provided explicitly. The main differences between the bulk and superlattice (k̂-ordered) Hamiltonians are contrasted. As an application, numerical calculations of the subband dispersion of G a N/I n x Al 1− x N quantum wells for various directions are presented and discussed. We show that inclusion of strain effects and the properly k̂-ordered Hamiltonian are essential in an accurate description of the valence subbands of quantum wells in these systems.