This paper is the second in a series describing the theory of photorefractive phase-conjugate oscillators. We apply the formulation developed in Paper I to study the threshold conditions for self-oscillation in the phase-conjugate mirror (PCM), the phase-conjugate resonator (PCR), and the phase-conjugate oscillator (PCO) by considering anisotropic four-wave mixing where the two counterpropagating off-axis pump beams are orthogonally polarized. We consider the two types of situations for orthogonally polarized pump beams corresponding to the two crystal families: one such as the ${\mathrm{Bi}}_{12}$${\mathrm{SiO}}_{20}$ crystal family (sillenite family) and the other such as ${\mathrm{BaTiO}}_{3}$ and the strontium barium niobate crystal family. Degenerate and nondegenerate self-oscillations are shown to occur for both these types for a number of practically important cases. Threshold conditions for oscillations are derived analytically under the assumption of undepleted pumps for most of these cases. It is shown that for the sillenite family of crystals, the coupling coefficient required for degenerate self-oscillation in PCR is one-half of that for PCM when the mirror is perfectly reflecting and when the pump beams have equal intensities. For PCO, the presence of the second mirror, however, increases the threshold value of the coupling coefficient for self-oscillation by a factor (1+${\mathit{R}}_{1}$${\mathit{R}}_{2}$)/(1-${\mathit{R}}_{1}$${\mathit{R}}_{2}$), where ${\mathit{R}}_{1}$ and ${\mathit{R}}_{2}$ are the power reflection coefficients of the mirrors. For the second type of crystal family, it is shown that PCM also can exhibit self-oscillation. The coupling coefficient required for degenerate self-oscillation in PCR is one-half of that for PCM when ${\mathit{R}}_{2}$=m and r=${\mathit{m}}^{\mathrm{\ensuremath{-}}1}$, where m and r are the ratios of the coupling coefficients of the backward and forward gratings and intensities of the backward and forward pumps, respectively.