The electronic structure of a quasi-two-dimensional hole gas near the interface of an AlGaN/GaN heterostructure is examined by calculating the valence band structure in the channel region in the framework of a six-band Rashba-Sheka-Pikus (RSP) Hamiltonian. Self-consistency in the Hartree approximation is achieved. Strain effects are included through deformation potentials and through the modulation of interfacial polarization charges associated with the piezoelectric nature of the constituent materials. It is found that for hole concentrations of 1013 cm-2, four subbands are partially populated. The effects of externally applied stress are then considered for the two distinct cases of hydrostatic stress and uniaxial stress applied parallel to the interface. While hydrostatic stress of practical magnitude appears to modulate the electronic structure only slightly, symmetry lowering uniaxial stress leads to significant changes in the population of the subbands and large dispersion anisotropies that should be detectable in piezo-mobility studies.