The Horde Expedition faction is one of the main factions in Northrend for the Horde. The Horde Expedition has 4 sub factions, The Hand of Vengeance, The Taunka, Warsong Offensive and The Sunreavers. To raise your faction with The Horde Expedition you can raise any of these 4 factions, or do the single daily for the Horde Expedition. The only daily that will raise your Horde Expedition faction is Blackriver Brawl in Grizzly Hills.
You can also do additional dailies in Grizzly Hills at the Blackriver Logging Camp, which will raise your faction with the Warsong Offensive. Which will intern, raise your faction with the Horde Expedition. For more information on the Grizzly Hill dailies click here.
The Horde Expedition does not have a quarter master, nor does it have a tabard. In addition if you're NOT wearing a tabard in a heroic instance you will gain faction with the Horde Expedition. The Horde Expedition calls it's main hub Warsong Hold in Borean Tundra.