To drag multiple nodes in Gephi, use the cylinder tool, which is part of the Dragging tool (Fist icon).
While the Dragging tool is selected, in the top left of the Graph window, next to the word "Dragging," click the blue word (Configure) as shown below
Set the diameter to something greater than one, and you'll see a grey disc that allows you to drag all nodes that are within the disc.
To "close" the tool, i.e. restore it to 1-pixel Dragging, Configure the diameter back to 1.