Multistage interconnection networks (MINs) are among the most efficient switching architectures in terms of the number of switching elements (SEs) used. For optical MINs (OMINs), two I/O connections with neighboring wavelengths cannot share a common SE due to crosstalk. In this paper, we focus on the wavelength dilation approach, in which the I/O connections sharing a common SE will be assigned different wavelengths with enough wavelength spacing. We first study the permutation capacity of OMINs, then propose fast parallel routing and wavelength assignment algorithms for OMINs. By applying our permutation decomposition and graph coloring techniques, the proposed algorithms can route any permutation without crosstalk in wavelength-rearrangeable space-strict-sense Banyan networks and wavelength-rearrangeable space-rearrangeable Benes networks in polylogarithmic time using a linear number of processors.