The far-field second-order radiation pattern from a wavelength-scale, InP-based photonic crystal microcavity that confines light in three dimensions is measured when excited on resonance by 300 W of continuous-wave power from a laser diode. The measurements are accurately simulated using the finite-difference time-domain method, showing that both absorption and scattering play significant roles in determining the pattern of the radiation. The results show that the bulk second-order nonlinear susceptibility mediates the nonlinear process. In a separate set of experiments, a short-pulse laser is used to simultaneously populate two distinct modes of a similar microcavity. The detected second-order spectra show features due to the second harmonic generated by each mode, as well as the sum-frequency generation due to nonlinear intermode mixing. The key phenomena that determine the second-order response of these fundamentally small optical cavities are identified.