Most of southern Eriador was largely unpopulated by the War of the Ring, but this was certainly not always so. Hollin (also called Eregion) was a great elvish kingdom during the Second Age, but after it was attacked and destroyed by Sauron in the mid-Second Age it was left uninhabited. Even so, when the fellowship travelled through the area on their way to Moria it was described as a pretty pleasant place.
Further south we find a slightly different story. Minhiriath to the west and Enedwaith to the east were both once populated by large numbers of men (and women, you get what I mean.) They were, like the Rohirrim, sort of cousins to the Edain - all descended from the same original group of men, but separated by their travels in the First Age. And the land itself was almost entirely forested - all part of the same primeval forest that stretched from Fangorn to the Old Forest and beyond.
However, when the Numenoreans started exploring Middle Earth, the coast of southern Eriador was some of the first territory they explored. Not recognizing the language of the indigenous people, they were labelled Men of Darkness, and the Numenoreans started deforesting the area in order to use the lumber to build more ships. Those local men who fought back were persecuted or driven out (some fled to the cape of Eryn Vorn.) When Sauron attacked Eregion later on, many of the folk of Minhiriath and Enedwaith supported him, hoping he would get rid of the Numenoreans. However, it was all for nothing since Sauron himself burned much of the remaining forest down during his assault.
In the Third Age parts of Minhiriath and Enedwaith were claimed by Arnor or Gondor. But after thousands of years of war (Arnor’s conflict with Angmar in the north, and the Dunlending’s conflict with the Rohirrim in the south) as well as the Great Plague and devastating floods after the Fell Winter most of the region was largely depopulated. By the time we get to the late Third Age the only mentioned groups of people are some secretive forest-folk in Eryn Vorn, the Dunlendings in the east, and some “barbarous fisher-folk” along the coast. After the War of the Ring, Aragorn claimed Minhiriath as part of the Reunited Kingdom.
SOURCES: LotR, LotR Appendices, The Unfinished Tales (“Aldarion and Erendis”, “The History of Galadriel and Celeborn”)