c. 1300, from late Old English tadige, tadie, of unknown origin and according to OED with no known cognates outside English. Applied to loathsome persons from 1560s. Toad-strangler "heavy rain" is from 1919, U.S. Southern dialectal.
monster of Greek mythology having a lion's (winged) body and a woman's head; she waylaid travelers around Thebes and devoured those who could not answer her questions; Oedipus solved the riddle and the Sphinx killed herself. In English from early 15c., from Latin Sphinx, from Greek Sphinx, said to mean literally "the strangler," a back-formation from sphingein "to squeeze, bind" (see sphincter).
There also was an Egyptian form (usually male and wingless); in reference to this it is attested in English from 1570s; specific reference to the colossal stone one near the pyramids at Giza is attested from 1610s. Transferred sense of "person or thing of mysterious nature" is from c. 1600. The proper plural would be sphinges. As adjectives in English, sphingal, sphingian, sphingine, sphinxian, sphinxine, and sphinx-like all have been tried.
"of Scotland," 1590s, a contraction of Scottish. As a noun, by 1743 as "the people of Scotland collectively;" 1700 as "the sort of English spoken by the people of Scotland."
Scots (mid-14c.) is the older adjective, which is from Scottis, the northern variant of Scottish. Scots was used in Scottish English until 18c., then Scotch became vernacular, but in mid-19c. there was a reaction against it because of insulting and pejorative formations made from it by the English (such as Scotch greys "lice;" Scotch attorney, a Jamaica term from 1864 for strangler vines).
Scotch-Irish is from 1744 (adj.); 1789 (n.); more properly Scots-Irish (1966). Commercial Scotch Tape (1945) was said to be so called because at first it had adhesive only on the edges (to make it easier to remove as a masking tape in car paint jobs), which was interpreted as a sign of cheapness on the part of the manufacturers. It had become a verb by 1955 and for a time was often printed without capitals.