Lol, this is like the Ame-no-Habakiri situation all over again.
When Oden cut Kaido with 2 swords, it was still described as Enma being the only sword to have cut him.
Now we have Zoro cutting Kaido with 3 swords, and Enma is the highlighted one.
So what do we conclude?
Also, like said above. If the haki is "Oden's", then why is it so strange for Kaido?
Shouldn't it be familiar haki rather than strange haki?
When Kaido notices the sword, his conclusion is that the stinging sensation is a result of the sword, not because of Oden's haki.
It's really shaping up to be that Enma was just created special rather than Oden himself making it special.