Traveling between Stranglethorn Vale and Orgrimmar is no small task -- the two zones are on entirely different continents. Stranglethorn Vale plays host to the neutral pirate city Booty Bay as well as the level-85 heroic dungeon Zul'Gurub, which hosts two chances at mounts and troll-themed transmogrification gear. Getting to Stranglethorn Vale can be quick and easy or a bit of a chore, depending on the means of travel.
The quickest and easiest way to get to Stranglethorn from Orgrimmar is to hop aboard the zeppelin that makes regular trips between Orgrimmar and Grom'Gol Base Camp in Stranglethorn Vale. There are two zeppelin towers in Orgrimmar, located on the canyon ridges between the Valley of Strength and the Drag and accessible via numerous elevators in the Valley of Strength. The eastern tower serves Stranglethorn Vale and Undercity, with landing pads for each distinguished by the hanging banners.
There are a couple of other, less efficient ways to get to Stranglethorn Vale. A ship out of faction-neutral Ratchet in the Southern Barrens travels to Booty Bay. You can also hop on the zeppelin to Undercity, and then take a flight down to Stranglethorn Vale, so long as you have connecting flight points. Riding your mount or running from Undercity are also options, but the path is extremely long and convoluted, as Stranglethorn Vale is in the far south of the Eastern Kingdoms and Undercity the far north -- and there are many, many Alliance towns on the way to hamper your progress.