The generation of two idler waves inside a high birefringent (HiBi) optical fiber through three four-wave mixing (FWM) processes is studied theoretically. The coupled-equations for the field amplitudes are derived and analytically solved, in the co-polarized and orthogonal polarization schemes. The obtained solutions take into account the delayed Raman response of the medium. The polarization sensitivity of the generation of the idler waves is analyzed. Results show that the stimulated Raman scattering does not change the efficiency of the idler wave generation in the co-polarized scheme, whereas in the orthogonal polarization scheme that nonlinear process decreases the efficiency of the four-wave mixing processes. Results also show that this set of multiple four-wave mixing processes is physically quite different from the typical single or dual pump four-wave mixing configurations. Findings show that the power transfer from the pumps to the idler fields can lead to a monotonous growth, or a periodic evolution of the sidebands along the fiber. Results show that the process efficiency varies greatly with the angle between the two pump polarizations.