We study intermodal four-wave mixing (FWM) in few-mode fibers in the presence of birefringence fluctuations and random linear mode coupling. Two different intermodal FWM processes are investigated by including all nonlinear contributions to the phase-matching condition and FWM bandwidth. We find that one of the FWM processes has a much larger bandwidth than the other. We include random linear mode coupling among fiber modes using three different models based on an analysis of the impact of random coupling on differences of propagation constants between modes. We find that random coupling always reduces the FWM efficiency relative to its vale in the absence of linear coupling. The reduction factor is relatively small (about 3 dB) when only a few modes are linearly coupled but can become very large (> 40 dB) when all modes couple strongly. In the limit of a coupling length much shorter than the nonlinear length, intermodal FWM efficiency becomes vanishingly small. These results should prove useful in the context of space-division multiplexing with few-mode and multimode fibers.