We have investigated the effects of pressure and temperature on viscosity and self-diffusion coefficients of the o- (OX) m-(MX), and p-xylene (PX) isomers in the temperature and pressure range of 298-348 K and 0.1-100 MPa, respectively. The transport coefficients have been computed using equilibrium molecular dynamics and the Green-Kubo formalism. The xylene isomers are described as multisite rigid molecules interacting with the OPLS force field. Computed densities and viscosities are in good agreement with experimental data and a correlation based on the rough hard-sphere theory. For each studied state point, the OPLS model is able to reproduce the relative order of densities and viscosities of the isomers. Using both sets of computed viscosity and self-diffusion data, we show that for xylene isomers the Stokes-Einstein (SE) relation is valid at the molecular level. Effective hydrodynamic diameters of isomers obtained from SE relationship are noticeably different. Finally, we discuss the influence of electrostatic interactions and mass distribution on transport properties and on the SE effective hydrodynamic diameter.