1520s, "miscellaneous collection," a humorous mock-Latin coinage from Latin omnium "of all things" (genitive plural of omnis; see omni-) + a feigned Latin form of English gather. Earlier form was omnegadrium (early 15c.), omnigatherum.

c. 1600, Latin, literally "a sound mind in a sound body," a line found in Juvenal, "Satires," x.356.

Mens sana in corpore sano is a contradiction in terms, the fantasy of a Mr. Have-your-cake-and-eat-it. No sane man can afford to dispense with debilitating pleasures; no ascetic can be considered reliably sane. Hitler was the archetype of the abstemious man. When the other krauts saw him drink water in the Beer Hall they should have known he was not to be trusted. [A.J. Liebling, "Between Meals," 1962]

1929 (in advertisements for "Air Wonder Stories" magazine), though there is an isolated use from 1851. See science + fiction. Earlier in same sense was scientifiction (by 1926). Abbreviated form sci-fi is by 1955. 

Latin, literally "in memory of," from accusative of memoria "memory" (from PIE root *(s)mer- (1) "to remember"). The phrase was much-used in Latin writing; Tennyson's poem of that name (published in 1850) seems to have introduced the phrase to English.

1761, "any disabled person or thing;" especially Stock Exchange slang for "defaulter."

A lame duck is a man who cannot pay his differences, and is said to waddle off. [Thomas Love Peacock, "Gryll Grange," 1861]

Sometimes also in naval use for "an old, slow ship." Modern sense of "public official serving out term after an election" is recorded by 1863, American English. The quote attributed to President Lincoln ("[A] senator or representative out of business is a sort of lame duck. He has to be provided for") is from an anecdote of 1878.

It is well known to everybody who knows anything of its history, that this court [Court of Claims] was made a sort of retreat for lame duck politicians that got wounded and had to retreat before the face of popular condemnation. That is just exactly what it was for, a safe retreat for lame ducks; and it was so filled up; (etc.) [Sen. John P. Hale, New Hampshire, Congressional Globe, Jan. 12, 1863, p.271]

"a tidal river," 1650s; see salt (n. ) + river. as a proper name, it was used early 19c. with reference to backwoods inhabitants of the U.S., especially those of Kentucky (there is a Salt River in the Bluegrass region of the state; the river is not salty, but salt manufactured from salt licks in the area was shipped down the river). The U.S. political slang phrase to row (someone) up Salt River "send (someone) to political defeat" probably owes its origin to this geographical reference, as the first attested use (1828) is in a Kentucky context. The phrase may also refer to the salt of tears.