For your purposes, it is better to use a screw extruder. Ultrasound will break the bonds of the polymer, and magnetic stirring will be weak to create a homogeneous mass. Extruder see the link
This depends on the viscosity of the solution under consideration. If the resin viscosity is not too high then a combination of ultrasonication and magnetic stirrer based mixing will be fruitful. In cases where the viscosity is very high use of suitable easily volatile solvent will be helpful in lowering the viscosity so as to get effective dispersion. However solvent removal will be a major challenge. In the case of solids, use of a hakke mixer will be helpful.