Common origin of multi mesh character

Set the origin of your armature object.

Don't have unity to test atm, (not since I quit windows for ubuntu) but IIRC the origin is the origin of the armature object.

2.8 example, cube is parented to armature as though it was body mesh

Select the armature in object mode, set the 3D cursor to where you wish the origin to be. In image example it's simply cursor to origin ShiftC. Select origin to 3D cursor from the set origin menu. (In 2.7x Object > Transform > Origin to 3D Cursor)

Now this is going to mess up the location of all children. In the case above I have selected the cube (it's the "body" of the armature for example sake) and clear the parent inverse to move it back. AltP Ckear Parent Inverse.

This however may depend on how the mesh objects were positioned as children to the armature. in which case selecting and translating is another option.

Also to move all meshes as well to have new origin as origin follow @FFeller's answer for meshes and clear parent inverse.

Hmmm, beginning to recall might actually be the root bone location. In which case, in bone edit mode, add a new bone at (0, 0, 0) and make it the parent bone of what is current root bone (probably hips)

Every mesh have an own origin. In Object mode set the cursor to 0,0,0 then select every mesh you want then click on Object>>Transform>>Origin to 3D cursor

The problem also can be in Unity.