Easterlings of the First Age
During the First Age, the term was applied to the sons of Bór and Ulfang, or the Swarthy Men, who came into Beleriand much later than the Edain, and who were for a part secretly in league with Morgoth.
The Easterlings of the First Age should not be confused with those of later ages. The term in the First Age was used to refer to any peoples who came from the east of the Ered Luin, and as such, the Easterlings of the First Age could well have come from Eriador, rather from the further east in the Wilderland of the area of the Sea of Rhûn.
Sons of Bór
Bór was a leader of Men who came into Lothlann, Beleriand, in the year 463. His sons were Borlach, Borlad and Borthand. Bór was welcomed by Maedhros, who gave him and his followers land north of the March of Maedhros, and south of it. Bór and his sons swore allegiance to Maedhros, and remained faithful, though he was told by Morgoth to betray the banner of Caranthir. All of them were wiped out during the Nirnaeth Arnoediad.
Sons of Ulfang "the Accursed"
Ulfang also came in Lothlann, Beleriand, in 463, shortly after Bór. He was the father of Ulfast, Ulwarth, and Uldor. Ulfang was welcomed by the sons of Fëanor, and he and his sons swore allegiance to Caranthir. They were given lands to dwell in the north and south of the March of Maedhros. Ulfang and his sons were secretly in the employ of Morgoth, and betrayed the Eldar and Edain during the Nirnaeth Arnoediad in what is now known as the Treachery of Men.
Easterlings of the Third Age
In the third age, the Easterlings were a significant threat to Gondor; they were a more regimented force than the Orcs or even the Haradrim. It is likely that Sauron drew much of his inspiration for his Orc armies from these wicked men. Sauron suffered a harsh and heavy defeat from the Last Alliance, who vanquished his numerically superior Orcs with a ranked and ordered army. The Easterlings were all this and more, so Sauron greatly valued his alliance with the men of Rhûn.
The weapons that the Easterlings used were primarily jagged spears, making them especially effective against cavalry, as well as a shorter, odd, glaive-like version used for close combat. They also were known to run their foes down in great Wains, or wagons.
Main Article: Wainriders
The Wainriders were a confederation of Easterling tribes who were united by their hate of Gondor, fueled by the dark lord Sauron. Following the Great Plague which weakened Gondor, they started their attacks in Third Age 1856, defeating the Gondorian army and killing king Narmacil II. They rode in great wagons and chariots (which gave them their name), and raided the lands of Rhovanion, destroying or enslaving its people. Gondor gradually lost all of its possessions east of Anduin to them. The thirtieth king of Gondor, Calimehtar son of Narmacil, defeated the Wainriders at the Field of Celebrant, buying some rest for his land. However the Wainriders struck back in 1944, allying themselves with the Haradrim of Near Harad and the Variags of Khand. They managed to kill king Ondoher and both his sons, but instead of riding on to Minas Anor and taking the city, they paused to celebrate. Meanwhile, general Eärnil of Gondor's southern army had defeated the Haradrim and rode north to defend his king. He came too late to rescue Ondoher, but managed to decisively defeat the Wainriders. Eärnil was later crowned king. After this defeat the might of the Wainriders was broken, and they retreated east. They still held Rhovanion, but never troubled Gondor again. It later turned out that their attacks were staged by Sauron to allow him to reclaim Mordor while Gondor's watch was diverted.
Main Article: Balchoth
The Balchoth were a fierce race of Easterlings, who attacked Gondor while under orders of Dol Guldur. In 2150 they overran the plains of Calenardhon and almost destroyed the army of the Ruling Steward Cirion, but were defeated by the Éothéod under Eorl the Young. Like the Wainriders they rode in chariots and wagons, and they may have been descendants of this people.
Main Article: Variags
The Variags (in the real world, this is another name for the Varangians) were from Khand, and they first appeared in the West in 1944 of the Third Age, fighting alongside the Wainriders. They later appeared during the battle of the Pelennor Fields. Little was known about them, but they appeared to be a race of horse-men much like the Rohirrim, although they were fiercely loyal to Mordor.