The dragging will be a bit more tricky because you need to work out where would the x/y positions of the mouse on the screen (screen space) will be in the 3D world, then you will need to cast a ray and check if it intersects the object you want to drag. I presume this will be a different question.
Setting object hierarchy is fairly simple.
As you hinted, you will use a THREE.Object3D instance to nest objects into using it’s add() method. The idea is that you will use a Mesh for objects that have geometry, and Object3D instances, where you simply need to nest elements.
group = new THREE.Object3D();//create an empty container
group.add( mesh );//add a mesh with geometry to it
scene.add( group );//when done, add the group to the scene
Update
As Nick Desaulniers and escapedcat point out, THREE.Group now provides the functionality you need. The included code example:
const geometry = new THREE.BoxGeometry( 1, 1, 1 );
const material = new THREE.MeshBasicMaterial( {color: 0x00ff00} );
const cubeA = new THREE.Mesh( geometry, material );
cubeA.position.set( 100, 100, 0 );
const cubeB = new THREE.Mesh( geometry, material );
cubeB.position.set( -100, -100, 0 );
//create a group and add the two cubes
//These cubes can now be rotated / scaled etc as a group
const group = new THREE.Group();
group.add( cubeA );
group.add( cubeB );
scene.add( group );