This appears to be the main quest vain for the zone, so be prepared for a long trip. I'll update as more information comes to light or changes. Please post replies for corrections.
While you don't need it to start the chain, you may as well start in the beginning.
Warchief's Command Board Quest: Warchief's Command: Azshara!
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Garrosh Hellscream Quest(Goblin): Report to the Labor Captain (Goblin, step 6 of chain She Loves Me, She Loves Me Not!)
1. Quest Hub: Orgrimmar Rear Gate
Labor Captain Grabbit starts with the Quests: Runaway Shredder! & The Captain's Logs & Up a Tree.
Completing Unlocks Quest: Report to Horzak.
2. Quest Hub: Orgrimmar Rocketway Exchange
Horzak Zignibble gives the Quests: Basilisk Bashin' & Stone Cold.
Completing Continues the Stone Cold Chain: The Perfect Prism, Prismbreak, Refleshification.
At his quest hub you must also complete the quests given by Foreman Fisk: A Quota to Meet.
Private Worcester now gives the Quest: Another Warm Body which send you to...
3. Quest Hub: Forlorn Ridge
Here Commander Molotov gives you the Quest: Hand-me-downs.
You must also finish the other quests at this hub given by Glix Grindlock (Military Breakthrough, and later In The Face!) & Xiz Salvoblast (First Degree Mortar).
Molotov now has the Quest: Profitability Scouting & Private Chat.
4. Quest Hub: Bilgewater Harbor
At this point you can head to Bilgewater Harbor and find a Wrenchmen Recruitment Poster for the Quest: Operation Fishgut, leading to Rapid Deployment, and There Are Many Like It.
5. Quest Hub: The Shattered Strand
Now that you're on The Shattered Strand seek out Lieutenant Drex for the Quest: Mop Up. You must also finish the quest of nearby Sergeant Hort (Halo Drop).
Drex now offers the Quest: Field Promotions sending you to...
6. Quest Hub: Ruins of Eldarath
Pick up every quest at the hub, from Captain Tork (Still Beating Heart), Sergeant Zelks (Extermination, Head of the Snake, Ticker Required), and Tora Halotrix (Handling the Goods).
Once these are finished, Tork offers the Quest: Shore Leave, a simple turn in.