Non-axisymmetric free-boundary equilibrium computations are shown to represent nonlinearly saturated external kink modes and external kink-like sidebands coupled to pressure-driven infernal modes. In this study of edge harmonic oscillations associated with QH-mode plasmas, two different driving mechanisms for external kink type-modes are identified. It is found that standard current-driven external kinks are linearly unstable, and nonlinearly stable in a wide parameter range, especially where q(edge) less than or similar to m/n. But, where standard current-driven kinks are linearly stable coupling of pressure-driven infernal modes can cause instability, and their upper sideband drives edge corrugations that appear to have external kink features. Both types of modes are identified with the VMEC equilibrium code, and the spectra are compared favourably with those of linear numerical approaches and analytic methods. Pressure-driven external infernal modes are shown to robustly occur in sophisticated modelling where the separatrix effect on the q profile is accounted for.