There are two distinct races of Straw Men.
Sateshrian Returned Strawmen
The magic to create the Sateshrian Returned Strawmen appeared sometime during the First Chaotic Period. Though the Sateshrian culture disappeared, the magic and the name stuck. Though they can be created by normal mages, the magic that powers them is in some way related to Necromancy, as a vital component is the skull of a sentient being. The rest of the body is comprised of an enchanted clay-like material on a wooden or stone skeleton. Various enchanted items(such as a stone for a heart) are placed inside the chest cavity. The power source draws on necromanic principles, harvesting energy from a soul in the Underworld.
The knowledge of how to create Strawmen persisted all the way through to the end of the Second Chaotic Period. With the war over there was no longer a need to create new ones(though some attempts were made to provide a source of cheap labor). Having fought beside many Strawmen in his day, Eieber banned the creation of them and declared them free peoples. History does not record what happened to the remaining Strawmen, though it is not thought that any limit existed on their lifespan.
The Straw Men were a race of golems created by the Iname, as part of their ultimate plan for vengence. What the Straw Men did not know, however, was that the Fall of Roads had happened and that the Eladamri no longer existed.
The Straw Men were created sometime during the Roads War, and laid down in various deep underground chambers (one such beneath the land of Rowen). Upon 'activation' the Straw Men would then begin one plan or another to wage war on the Eladamri.
Various uprisings are known throughout history, including a major one during Hunter's time. The Straw Men were also most likely responsible for the creation of eldritch SkyShips used throughout the Mage Wars.
The Straw Men are human-shaped though not always humanoid. They are made from a sort of semi-living clay, and are sentient, complete with free-will.