Old English streaw (rare) "stems or stalks of certain species of grains," apparently literally "that which is scattered or strewn," related to streowian (see strew), from Proto-Germanic *straw- "that which is scattered" (source also of Old Norse stra, Danish straa, Swedish strå, Old Saxon stro, Old Frisian stre, Old Dutch, Old High German stro, Dutch stroo, German Stroh "straw"), from PIE root *stere- "to spread." The notion perhaps is of dried grain stalks strewn on a floor as carpeting or bedding.
As a type of what is trifling or unimportant, attested from late 13c. Meaning "hollow tube through which a drink is sucked" is recorded from 1851. To draw straws as a means of deciding something is recorded from 1779 (the custom probably is older). As an adjective, "made of straw," mid-15c.; hence "false, sham." Straw poll is from 1932; earlier straw vote (1866). Straw hat first attested mid-15c. To clutch (or grasp or catch) at straws (1748) is what a drowning man proverbially would do. The last straw (1836 apart from the full phrase) is from the proverbial image: "it is the last straw that breaks the camel's back" (or, less often, the mare's, the horse's, or the elephant's), an image in use in English by 1755.
Let it not, however, be inferred that taxation cannot be pushed too far : it is, as the Oriental proverb says, the last straw that overloads the camel ; a small addition, if ill-timed, may overturn the whole. ["The Scots Magazine," April 1799]