We present one-dimensional hydrodynamical simulations including radiative losses, of internal shocks in the outflows from classical novae, to explore the role of shocks in powering multi-wavelength emission from radio to gamma-ray wavelengths. Observations support a picture in which the initial phases of some novae generate a slow, equatorially-focused outflow (directly from the outer Lagrange point, or from a circumbinary disk), which then transitions to, or is overtaken by, a faster more isotropic outflow from the white dwarf which collides and shocks the slower flow, powering gamma-ray and optical emission through reprocessing by the ejecta. However, the common occurence of multiple peaks in nova light curves suggests that the outflow's acceleration need not be monotonic, but instead can involve successive transitions between "fast" and "slow" modes. Such a time-fluctuating outflow velocity naturally can reproduce several observed properties of nova, such as correlated gamma-ray and optical flares, expansion of the photosphere coincident with (though lagging slightly) the peak flare luminosity, and complex time-evolution of spectral lines (including accelerating, decelerating, and merging velocity components). While the shocks are still deeply embedded during the gamma-ray emission, the onset of ∼ keV X-ray and ∼ 10 GHz radio synchrotron emission is typically delayed until the forward shock of the outermost monolithic shell (created by merger of multiple internal shock-generated shells) reaches a sufficiently low column through the dense external medium generated by the earliest phase of the outburst.