Spelling with J- predominated from 16c. Replaced Old English Iudeas "the Jews," which is from Latin. As an offensive and opprobrious term, "person who seeks gain by sordid means," c. 1600. Jews' harp "simple mouth harp" is from 1580s, earlier Jews' trump (1540s); the connection with Jewishness is obscure, unless it is somehow biblical.
In uneducated times, inexplicable ancient artifacts were credited to Jews, based on the biblical chronology of history: such as Jews' money (1570s) "Roman coins found in England." In Greece, after Christianity had erased the memory of classical glory, ruins of pagan temples were called "Jews' castles," and in Cornwall, Jews' houses was the name for the remains of ancient tin-smelting works.
"to cheat, to drive a hard bargain," 1824, from Jew (n.) (compare gyp, welsh, etc.). "Though now commonly employed without direct reference to the Jews as a race, it is regarded by them as offensive and opprobrious" [Century Dictionary, 1902]. The campaign to eliminate it in early 20c. was so successful that people also began to avoid the noun and adjective, using Hebrew instead.
Now I'll say 'a Jew' and just the word Jew sounds like a dirty word and people don't know whether to laugh or not. [Lenny Bruce, "How to Talk Dirty and Influence People," 1965]
1610s, from French judaïque (15c.), and directly from Latin Iudaicus, from Greek Ioudaikos, from Ioudaios "Jew" (see Jew). Earlier in same sense was Judaical (late 15c.).