Random Raman lasers attract now a great deal of attention as they operate in non-active turbid or transparent scattering media. In the last case, single mode fibers with feedback via Rayleigh backscattering generate a high-quality unidirectional laser beam. However, such fiber lasers have rather poor spectral and polarization properties, worsening with increasing power and Stokes order. Here we demonstrate a linearly-polarized cascaded random Raman lasing in a polarization-maintaining fiber. The quantum efficiency of converting the pump (1.05 μm) into the output radiation is almost independent of the Stokes order, amounting to 79%, 83%, and 77% for the 1(st) (1.11 μm), 2(nd) (1.17 μm) and 3(rd) (1.23 μm) order, respectively, at the polarization extinction ratio >22 dB for all orders. The laser bandwidth grows with increasing order, but it is almost independent of power in the 1-10 W range, amounting to ~1, ~2 and ~3 nm for orders 1-3, respectively. So, the random Raman laser exhibits no degradation of output characteristics with increasing Stokes order. A theory adequately describing the unique laser features has been developed. Thus, a full picture of the cascaded random Raman lasing in fibers is shown.