Upon release Siege of Mirkwood concluded the Mines of Moria story, the second of the Epic books overall. The third Epic story line, Allies of the King, launched shortly afterwards and focused on the Grey Company, being completely unrelated to Mirkwood.
 Volume III: Allies of the King
Book 1 - Oath of the Rangers
Elrond received a mysterious message from Galadriel, telling him to gather the Rangers of the North and send them to Rohan to help Aragorn. The player is summoned to the Last Homely House and given a list of Rangers to recruit: Radanir of the Trollshaws, Candaith of Weathertop, Saeradan of Bree-Land, Halros of the Shire, Halbarad from Esteldin, Calenglad from Evendim, Lothrandir from Forochel and finally Corunir and Golodir from Angmar. With the exception of Radanir, all Rangers are the ones player have interacted with during Epic Volume I. Joined by others of their kin, they form the Grey Company and meet Elrohir, Elladan and Lady Arwen, who passes Halbarad the banner she has made for Aragorn.
Book 2 - Ride of the Grey Company
Setting forth from Rivendell, the Grey Company begins the journey south. While passing the Ring-Forges of Eregion, Halbarad asks a Dwarf-Jeweler to craft fake copies of the Ring of Barahir, in order to confuse their enemies and buy Aragorn time, should a member Grey Company be captured. Arriving in the lands of Enedwaith, the Rangers are trying to make peace with the local tribes and eventually discover an old and confused Dwarf Nár, father of Ollfardh and one-time companion of Thrór. To everyone's amazement, he knows about the secret road the Company is planning to take. A man of Dunland named Wadu offers his help to the Grey Company, yet is soon found dead. Upon delivering news to his relatives, the player learns that Wadu saw to earn honor in the eyes of his father, who viewed him weak and his sister, Nona, as more of a warrior than her brother ever was.
Book 3 - Echoes of the Dead
Wadu's family learns that before his death he accomplished an act of great honor by slaying a Gwiber-Drake, which no Dunlending could do alone. His father is ashamed and his sister offers to join Grey Company to wage war against Saruman, to which Halbarad absolutely refuses. While investigating who can be trusted and who can't, the Rangers receive word that of a band of Oathbreakers from Erech in Enedwaith. An attempt to remind them of their Oath to Isildur fails horribly when Candaith is killed. Halbarad wants to have nothing more to do with this land and leads the company on to Dunland, but as the player leaves Nár, the Dwarf reveals that Saruman the White had a hand in these events all along.
The Epic story continues with the Rise of Isengard expansion - following Siege of Mirkwood there is no longer direct correlation between expansions and Epic Volumes.
Book 4 - Rise of Isengard
Passing into the lands of Dunland, the Rangers investigate the loyalties of the local tribes of Dunlendings. Some are fiercely loyal to Saruman, other openly oppose him and many have not yet been convinced to do either. The Falcon-clan of Tur Morva village offers the Rangers shelter in exchange for their help against Saruman. The Rangers busy themselves with preparations for war while the player is send to scout the rest of Dunland. Finding a surprise ally in Nona, who insists that she does not need Halbarad's permission to travel over her own land, the player and the Rangers come into first contact with Rohirrim. Riders led by Grimbold hold the Fords of Isen against inevitable assault, while Théodred, son of Kind Theoden, leads a smaller scouting party into the lands of the Dunlendings, who have been sworn enemies of Rohan for centuries. Returning to village of Tur Morva, the player finds a betrayal waiting for them: the clan decided that more is to be gained by siding with Saruman than by opposing him. Grey Company is caught unprepared, many Rangers are killed and the rest captured. The player and Ranger Lothrandir are send directly to Isengard as a gift to Saruman. Separated from the Ranger, the player is send working into the pits, observed by merciless Uruks. Using the dislike of Uruks for each other, the player fakes a total submission and is eventually allowed more freedom, as none believes him able to escape any longer. The player finds other prisoners, among them captured Rohirrim and Dunlendings - sworn enemies once, both find something in common after been made slaves to Saruman. Staging a diversion and freeing many prisoners at once, the player is able to sneak past confusion and escape Isengard. Théodred offers Rangers Saeradan and Radanir help in rescuing their captive friends and avenging the betrayal. The player and Rohirrim storm the village of traitors and rescue many Rangers, including Halbarad and the sons of Elrond. Yet they are still outnumbered - the leader of the traitorous clan gloats over Ranger's weaknesses and allows them to leave, telling them to spread the tale of how the Falcon-clan beat them. Of almost 60 named Rangers barely 30 made it out alive: Halbarad takes an oath to avenge the traitors and proclaims himself in eternal debt to Théodred, before planning the next move.
Source: Wikipedia, "The Lord of the Rings Online: Siege of Mirkwood", available under the CC-BY-SA License.