What do you mean you didn't learn the shout? It's not highlighted in your shouts menu? It stands to reason that you can't use the shout until the scripted sequence at the Great Porch (or whatever it's called) and then not again until you advance the MQ to a certain point.
I mean, I get past the dialogue with Paarthurnax where I learn the shout to call Odahviing. The questline for it also tells me to procede to Whiterun to call Odahviing. But no such shout exists in my menu. That's a dead end, right?
The only thing I can think to do is reload my save from before the dialogue with Paarthurnax and experimenting for a way around this.
I'm currently at the point where the Blades want me to kill Paarthurnax, and I told Greybeard Whatshisname that I haven't decided on it yet. I've also tried talking to Paarthurnax with and without Dawnguard installed.
...You're not saying that the Odahviing shout only shows in the menu when the main quest needs to advance???? I don't recall that from my first playthrough.