As you state, in an electric field, a polar molecule such as methanol or water, having an uneven charge distribution, is attracted (or repelled) by an electric field. This orients the molecule, but is not primarily responsible for the attraction of the bulk substance.
An electric field causes a force on even a nonpolar molecule such as methane or sulfur, though. You can pick up powdered sulfur with a charged piece of plastic because of electrostatic induction, which moves electrons in the bulk material.
This induced charge is similar to the effect of moon (and sun) on tides, pulling the water underneath the moon more strongly than it pulls on the more distant core of the earth, and on the core more strongly than on the ocean on the opposite side of the planet, causing uneven distribution of the water. In a similar way, an external field causes an uneven distribution of charge.