In general, it is not possible to observe simultaneously all nonlinear effects described by the nonlinear polarizations, because usually only one nonlinear process is phase-matched.
In nonlinear nano-optics, since the wave phase-matching between interacting optical fields does not affect the nonlinear optical interactions, is it necessary to achieve phase-matching ?
The role of phase matching is important for any nonlinear generation that occurs as a driving field propagates -- e.g. through a crystal, or along a waveguide. The point to remember that essentially "all" nonlinear effects are *always* generated at each point along that propagation, but only the phase matched ones accumulate. The non phase matched ones are generated with different and oscillating phases, and so will average to almost zero. Looking up how quasi-phase matching as used in chi(2) materials might be helpful for you.
If the nonlinear material is thin (much thinner than a wavelength), so that generation is sudden and brief, then this averaging effect has no time (or distance) to act over. In such a case phase matching is irrelevant, unless e.g. you plan to propagate through a series of carefully spaced thin surfaces.
As a final note, if considering generation from propagation through a thin sheet, it may be that you want to consider a full time-dependent model of the nonlinearity, and not assume it is perturbative - especially if e.g. this sheet is an engineered material (metamaterial) designed to have a very large nonlinearity.
At nano-scale, the phase-matching can be replaced by the overlap between the resonances for the interacting wavelengths (both material resonances and resonances due to the geometry of any present nano-structures). Have a look at this paper: https://www.nature.com/articles/s41467-018-04944-9
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