If you want to drag an individual linedef, you need to switch into linedef mode first (press 'L' on the keyboard, by default). If you want to drag the whole sector, you need to be in sector mode, although it sounds like you are already (press 'S'). Note that right-clicking always brings up a properties dialogue, either linedef- or sector-properties according to the current mode; to move, you have to right-drag the objects, without releasing the mouse-button.