What are these unsymmetrical parts at the tail of the Tupolev TU-144? On a recent trip to the Technikmuseum Sinsheim, I noticed that the back of the Tupolev TU-144 is not symmetric. 
Please take a look at the picture I took to understand what I mean:

(Please don't mind the crane, the Tupolev was getting cleaned that day)

Those parts most likely serve some aerodynamic/stabilizing purpose, but what exactly do they do? Why aren't they the same on both sides?
The four parts you're referring to contain the actuation mechanism for the rudder, similar to the wing pods that contain the flap actuation mechanism.

The reason they are not arranged symmetrically is that the rudder has two sections (you can see the 'cut' in the middle in your image)- apparently to provide redundancy and improve safety. So,each section has two actuation mechanisms on the same side, with both of them in opposite sides.

The Concorde had a similar arrangement, albeit with only a single mechanism on either side, as can be seen below.



By Simon Boddy, CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=31619795