Here is a way to do it:
Now your X object twists, but you must rotate it:
- In the Properties panel > Object > Transform, rotate your X object on the Z axis, for example:
- frame 0 = 0°
- frame 60 = -360°
To do the second twist (on the X axis), just disable the first Simple Deform modifier with a keyframe on its visibility (eye and camera icons) after the end of the twist, create a second Empty on the right or left of the X object, rotate this new empty 90° on the Y axis, give your X object a new Simple Deform modifier with this second Empty as the axis, and again, play with angles, rotation and keyframes.
Also, if you want to move your X object in your scene, parent your X object and its empties to a new empty.