I came across several bugs trying to complete this quest last night.

First, after settling a truce between Ulric and General Tullius, I am told to go to White Run and ask Jarl Grey Mane for help.
I talk to him in this hall and he mutters something about going to tell his men to get ready. He then proceeds to JUST STAND THERE.
If I activate a conversation with him again, he repeats the same line and continues to stand there. I tried Thum'ing him with Unrelenting Force to no avail, I then proceeded to get stabby in the hopes that he will follow me outside and activate the next steps and the cur just runs away in fear... I then hit upon an idea to WAIT for him to get his act together. 8hours later, thankfully, the quest arrow over his head had moved outside of the hall.

Yes, I exclaimed in a manly Nordic yelp. I follow the source to realize that the old !@#!#@!#@ Jarl is ASLEEP in his bed and still has not mustered his men.
I kicked his ass out of bed and follow him to the battlements to set the trap.

I used my Call Dragon Thum to no avail.
"Bueler? Bueler? Bueler? http://www.uesp.net/wiki/Skyrim:Odahviing? Anyone?"

Apparently, the trick here is to HOLD down the button to make the Shout louder...

Next, Odahviing approaches in a fury of wings and vengeance and I drop him with Dragonrend. I then proceed to hold his favorite Scooby snacks under his nose and have him follow me and spring the trap.

I approach under a flag of truce and offer to let him go if he helps me. After short comedic bit where I try to figure out HOW to let him go, seeing that you can't interact with the device holding him in place or shoot the chains with my bow action here style... Ends up I have to go walk up the hidden stair case and talk to a scared #!#!@less guard to let the dragon go...

We bump dragon fists and I let him go. He then proceeds to get all aggro on me, breathing fire, and being an all around obnoxious guest.

Looks like Jarl (Old Guy) decided that now was a good time to show off what a bad ass he is and attacks the dragon I have just made a deal with.
*facepalm*

I am the !@#!@#!@# Dragonborn old man! I will scoop your skull out with a spoon and use it for my chamber pot, you fool!

This whole quest is so totally janky. Come on Bethesda, you can do better than that!

*Yes I know I can leave the area and come back hours late to find a much more placid Odahviing quietly sipping tea and perusing a Reader's Digest, but seriously... @_@

Please do not post Spoilers in General.

People come to General to learn about the game without learning about what happens in the game. If they want to know about what happens, that is what the Cheats, Hints and Spoilers section is for.

Do not use quest details or location specific details related to quests/puzzles/NPCs in your posts in this section. General is for discussing gameplay and mechanics. General topics about the the game include but are not limited to races, items and their use, magic, enchanting, skills, character builds, criticism, praise, funny random things that happen, places from an esthetic standpoint and and other general topics.

Use the Spoilers Section if you have to post quest details or other spoilers or a thread about the same. This also includes console commands, and character build exploits.

I will move this now.

Sorry about that!

Sounds like quite a mess!

I did that quest with the original jarl, so I can't say much about yours.

But I have come across the same problem with a quest NPC not following their proper routes and stalling quests before.
Just recently I had it happen with the Vaermina quest, after speaking to Erandur he is supposed to walk up some stairs and unlock a door, but he stayed glued to the spot. First I tried starting the quest from scratch again, but reached the same point and he got stuck in place again.
I eventually used Unrelenting Force to toss him up the stairs and when I had tossed him up near the door he proceeded to unlock it.

It must bug out somehow and the game forgets to update the NPCs instructions.