As you said, vampire's Kenjuu are manifestation of their powers... In that sense, Kojou "can" controll all abilities that his Kenjuu have including Lightning, Barriers, Mist Control, etc.. (which he uses in Anime quite a lot). But he does not use all the abilities he has probably because he doesn't know how to use them...or something like that.
I would more believe that the familars of the fourth progenitor are representations of the powers of vampires, say Natra Cinereus represents a vampire's power to turn mist, or Sadalmelik Albus represents the healing factor of a vampire by turning back time, or Dabih Crystallus if the wiki is accurate represents a vampire's dominating or bewitching ability. The rest of the familars can represent the destructiveness of vampires. All in all his familars are extremely powerful as most can cover each others weakness with the downside of being hard to control. I am interested to see how Cain will counter balance him.