Another possibility is that Vader's phrenic nerves may have been damaged from his burns. The phrenic nerves stimulate the movement of the diaphragm, a muscular membrane that causes the lungs to fill and empty. Since the phrenic nerves come out of the protective spinal cord at the back of the neck, and Vader may have suffered serious burn damage there, we might theorize that severe heat damage destroyed the nerves and caused a partial paralysis. If this is the case, then Vader might need assistance to inflate and deflate his lungs.
Quadriplegics who suffer from a similar problem use a ventilator attached through a hole in the neck to the trachea. This means air enters and leaves the body below the vocal cords, never passing over them. In a more sophisticated design, a speaking valve can be incorporated into the tube, which allows air through the tube into the lungs, but prevents air from leaving by the same path. Vader may have a similar ventilation device. This would explain why his breathing seems independent of his speech. A person's voice with such a system can often be weak. Thus to project a commanding presence, Vader would need his voice augmented somehow.
The easiest method for Vader, though, would be to simply use the Force to pump air in and out of his lungs and move his burn-damaged limbs. But I guess even a lord of the Sith gets tired sometime.