In their earliest recorded history the Stoors, like the other Hobbits, lived in the Vale of Anduin. They were a riverside people that dwelt in the Gladden Fields, and were fishermen. They were broader in build than the other Hobbits, and had large hands and feet. This has led several Tolkien fans to refer to the Stoorish hobbits as "fake hobbits". Among the Hobbits, the Stoors most resembled typical Men (for as Tolkien later says, Hobbits were properly an offshoot of Men rather than a separate race, though they themselves considered themselves separate).
Stoors were the only Hobbits who grew facial hair, and only some of them could at that. A habit which set them apart from the Harfoots who lived in the mountain foothills, and the Fallohides who lived in forests far to the north, was that many Stoors used boats, and could swim. They also wore boots.
After the Harfoots had migrated westward, and the Fallohides followed them in 1150 of the Third Age, the Stoors long remained in the vale of Anduin, but between 1150 and 1300 they, too, migrated west. Unlike the other Hobbit-kinds they took the Redhorn Pass, ending up in Eregion and Dunland. Some Stoors went to the Angle south of Rivendell and mingled with the Harfoots and Fallohides that lived there, but most settled in the Swanfleet near Tharbad, which most resembled their old lands.
After 1300 when Angmar began to threaten Eriador, many Stoors fled south to their kin in Dunland, where they became a woodland people. Some few returned to the vale of Anduin and resettled the Gladden Fields, becoming the riverland people Déagol and Sméagol (Gollum) belonged to. This is evident from Gandalf's description I guess they were of hobbit-kind, akin to the fathers of the fathers of the Stoors in The Fellowship of the Ring. Some of these villages might have survived until the War of the Ring, when they were sought out by the Ringwraiths.
However, most Stoors fled to the north and west, ending up in the newly founded Shire around 1630. There they mingled with the Harfoots and Fallohides, becoming the Shire-folk. The Hobbits of the Eastfarthing remained very Stoorish in appearance and character, as did some of the Hobbits of Bree and Buckland. Some of the local names reflected their Southern origins, being in a language related to Dunlendish.