Two of today’s words are homophones (or heterographs if you prefer); the third is a common contribution from stupid autocorrect. The fourth is only barely a word.
Threw: the past tense of throw.
Through: to enter on one end and exit on the other or go from beginning to end.
Thorough: to do everything that needs doing, completely and with attention to detail.
Thru: a semi-literate shortened version of through, only permissible at businesses with a drive-up window.
Threw first appears before 1000, from the Middle English throwen, thrawen; it comes from the Old English thr?wan, meaning “to twist, turn”; you can trace it back through the Dutch draaien and German drehen, meaning “to turn, spin, twirl, whirl.” Somehow this comes from to the Latin terere and Greek teírein, which mean “to rub away.”
Through is a little older, before 900; it’s a Middle English variant of thourgh, from the Old English thurh. It comes from the same root word as the German durch and related to the Old English therh, which all come from the Gothic thairh, meaning “through.” Going back a little further, you get to the Old High German derh, meaning “perforated,” and the Old English thyrel, “full of holes.”
Thorough is also from before 900, from the Old English thuruh, which is a variant of thurh through.
If you say “he through a pumpkin at me,” you’re saying he either spied on you by looking through a jack-o-lantern or he crawled through one.
If you say “we went threw the costume box,” you’re saying you flung the costumes all over the attic.