Engineering nonlinear optical responses at the microscale is a key topic in photonics for achieving efficient frequency conversion and light manipulation. Gallium nitride (GaN) is a promising semiconductor material for integrated nonlinear photonic structures. In this work, we use epitaxially grown GaN microwires as nonlinear optical whispering gallery and Fabry-Perot resonators. We demonstrate an effective generation of second-harmonic and polarization-dependent signals of whispering gallery and Fabry-Perot modes (FPM) under near-infrared (NIR) excitation. We show how the rotation of the excitation polarization can be used to control and switch between Fabry-Perot and whispering gallery modes in tapered GaN microwire resonators. We demonstrate the enhancement of two-photon luminescence in the yellow-green spectral range due to efficient coupling between whispering gallery, FPM, and excitonic states in GaN. This luminescence enhancement allows us to conveniently visualize whispering gallery modes excited with a NIR source. Such microwire resonators can be used as compact microlasers or sensing elements in photonic sensors.