If all the layers to be moved are in the same workspace, select them, start editing and then move the collection.
If they are not in the same workspace, and you don't want to move them temporarily into one, you have a couple of options that aren't as easy but should work. One is to use the move option, and apply the same x and y move values to each layer in its own edit session. A second would be to find a shared vertice in each layer or temporarily add a feature to the layers to be moved that shares a vertice with say a point. Then in individual edit sessions select the features to be moved in that layer and snap the matching vertice in each to that point.