You can get virtually dry MeOH by distillation. However, you require a very, very long column and a careful, slow distillation to properly separate it from water (400mm at the least)... and a very accurate thermometer.
Yeah, MeOH is miscible with DCM and with toluene and with DCM/toluene. And water is miscle with MeOH. But MeOH/DCM/Toluene/water will form two layers. One with mostly water, some DCM, some toluene.. the other with mostly DCM and toluene and some water.