"sharp, shrill cry," 1550s, from screech (v.). Earlier scritch (1510s). In reference to a harsh, squeaking noise made by something, by 1882.
1846, from Latin sonantem (nominative sonans), present participle of sonare "make a noise, sound" (from PIE root *swen- "to sound"). As a noun from 1849.
"clamorous, noisy, boisterous, especially in opposition," c. 1600, from Latin obstreperus "clamorous," from obstrepere "drown with noise, make a noise against, oppose noisily," from ob "against" (see ob-) + strepere "make a noise," from PIE *strep-, said to be imitative (compare Latin stertare "to snore," Old Norse þrefa "to quarrel," þrapt "chattering, gossip," Old English þræft "quarrel"). But de Vaan writes, "It is uncertain that *strep- goes back to PIE, since it is only found in Latin and Germanic." Extended sense of "resisting control, management, or advice" is by 1650s. Related: Obstreperously; obstreperousness.
"loud, disorderly, confusing noise," 1560s, probably imitative. Klein and Century Dictionary compare Gaelic racaid "noise, disturbance," but OED says this "is no doubt from Eng."
Meaning "dishonest activity" (1785) is perhaps an extended sense, from the notion of "something going on" or "noise or disturbance made to distract a pick-pocket's victim." Or it might be from racquet, via the notion of "a game," or from or reinforced by rack-rent "extortionate rent." There also was a verb racket "carry on eager or energetic action" (1753), and the gangster sense might be via the notion of "exciting and unusual." Weakened sense of "way of life, one's line of business" is by 1891.