You can do it using a plane and adding it a screw modifier then a twist simple deform modifier:
The screw modifier need to have enough 'steps' (here 64) so that the shape can deform.
The simple deform modifier, twist mode, is set with an empty as axis origin. This empty is rotated 90° around Y.
We can notice that the twist enforce the screw effect, so that the twist is finally a combination of the angles of both modifiers (to be tune as you want).
Now, if you just duplicate the mesh and place the dupli on the side of the first one, the dupli will turn around it:
And if finally, you move the empty just between the two meshes, they twist around each other:
Edit: Of course Simple Deform is the easiest way to do it...
If you don't like the easy way you can do it with a spiral and a Curve modifier:
- Create your twisted object with a Simple Deform modifier.
- Array it if you want to make it longer.
- Create a Curve > Curve Spirals > Archemedian. Make it 360° or several times 360°. Put its origin on its bottom.
- Put your object at the same position as the spiral with a shiftS > Selection to Cursor.
- Give your object a Curve modifier with the spiral as Object.
- Link-duplicate both your object and your spiral with an altD, move it a bit so that it twist around the other. You can edit the object or the spiral the way you want, the modifications will be duplicated on the other object and spiral.