A ten-band k ∙p Hamiltonian for III-V-N dilute nitride semiconductor quantum wells (QWs) grown on the (11N)-oriented substrates is presented. The energy dispersion curves, optical transition matrix elements, internal piezoelectric field, and optical gain of InGaAsN/GaAs on the (110), (111), (113), and (11∞)-oriented substrates are investigated including band-anti-crossing, strain, and piezoelectric field effects. The band structures and optical gain are sensitive to the substrate orientation. The fundamental transition energy is the largest for the (111)-oriented QW and the smallest for (11∞)-oriented QW. The absolute values of internal piezoelectric field in the well and barrier layers reach the maximum for the (111)-QW, and zero for the (110) and (11∞)-oriented QWs. There exists an injection current density turning point. When the injection current density is below the turning point, the (111)-oriented QW has the largest peak gain. At the larger injection current density, the (11∞)-oriented QW has the largest peak gain.