Both up and out can be used in conjunction with the wazoo, and both imply too much of something. In this context, the wazoo is a slang term for the anus. The etymology of the term is uncertain. I have always felt that up the wazoo implied a more unpleasant situation than out the wazoo, but I'm sure that is simply a matter of personal preference. [cough].
Wiktionary has identical definitions for each term, and also makes note of the similarity to the phrase up/out the ying-yang [sic].
up the wazoo
1. (vulgar, idiomatic) up the ass; excessive or excessively; too much
e.g.: I'd go, but I'm sure they will charge up the wazoo for tickets.
out the wazoo
1. (vulgar, idiomatic) out the ass; excessive or excessively; too much
e.g.: I planted a few seeds and had radishes out the wazoo within a month.
An article in the Columbia Journalism Review provides some possible explanations for the origin of both the phrase and the word itself:
... the venerable Oxford English Dictionary weighs in. While it professes not to know the origin of “wazoo,” it says that others suspect it may come from the French oiseau, or bird, through a Louisiana Creole term, “razoo,” for raspberry. (Those with particularly fertile dirty minds may be able to make the connection.) It’s almost exclusively American.
The OED’s first two citations are telling in themselves. The first, in 1961, is from a University of California, Berkeley publication: “Run it up yer ol’ wazoo!” Its second citation is from a publication not known for its use of slang, The Wall Street Journal, in 1971: “Golf itself is quite safe, the greatest risk being the possibility of a long drive plunking some poor fellow in the wazoo.”
A post on grammarphobia.com mentions another possibility:
The Cassell’s Dictionary of Slang suggests that “wazoo” as a euphemism might be a variation on “gazoo” and “kazoo,” which had been put to similar uses in the 1960s. The OED also notes the similarities between the terms, and has citations for this slang usage of both “gazoo” (1965) and “kazoo” (1973).
Wikipedia offers a different explanation but, sadly, offers no reference or citation of any kind:
Slang for anus Originally derived from the Pama-Nyungan languages (the family of Indigenous Australian languages), and thought to refer to the anus of an animal, particularly the kangaroo.
The Facts on File Dictionary of Proverbs has the following (emphasis mine):
talk is cheap: [...] "What can you do?" "Go out Montana, just as soon as the weather is fit, and relocate the mine..." "Talk is cheap, but it takes money to pay for railroad tickets, went on Malone" (Horatio Alger, Joe the Hotel Boy, 1906) The proverb was first recorded in its current form in 1843 (T.C. Haliburton, Attaché), but the sentiment it expresses is of earlier origin.
Here is the relevant quotation from Haliburton's book, completely titled The Attaché; or, Sam Slick in England, and courtesy of Project Gutenberg:
"Minister," said Mr. Slick, "come, cheer up, it makes me kinder dismal to hear you talk so. When Captain McKenzie hanged up them three free and enlightened citizens of ours on board of the—Somers—he gave 'em three cheers. We are worth half a dozen dead men yet, so cheer up. Talk to these friends of ourn, they might think you considerable starch if you don't talk, and talk is cheap, it don't cost nothin' but breath, a scrape of your hind leg, and a jupe of the head, that's a fact.
Haliburton was a novelist, and Sam Slick seems to have been his primary literary foil, much like Hercule Poirot and Tom Ripley became for Agatha Christie and Patricia Highsmith, respectively. From Wikipedia (emphasis mine):
Sam Slick was a character created by Thomas Chandler Haliburton, a Canadian judge and author. With his wry wit and Yankee voice, Sam Slick of Slicksville put forward his views on "human nature" in a regular column in the Novascotian, beginning in 1835. The twenty-one sketches were published in a collection titled The Clockmaker, or the Sayings and Doings of Samuel Slick of Slicksville, First Series in 1836, supplemented by an additional 12 unpublished or new sketches. The book was Canada's first international bestseller and was hugely popular, not only in Nova Scotia but also in Britain and the United States....Slick’s wise-cracking commentary on the colonial life of Nova Scotia and relations with the U.S. and Britain struck a note with readers, leading to a second series in 1838 and a third in 1840.
The opening paragraph from a biography of Haliburton, titled Inventing Sam Slick: a biography of Thomas Chandler Haliburton, gives one a clue to Slick's renown:
For fifty years after 1837, Sam Slick the Clockmaker was the most
celebrated literary Yankee of the day. The mere mention of him
brought smiles to the faces of readers in Victorian Britain.
He struck the funny bone of a nation with his barrage of Yankee slang.
Few readers knew that his creator, Thomas Chandler Haliburton,
was a gentleman, a Judge of the Inferior Court of Common Please
in the colony of Nova Scotia. Today, Sam Slick is still more famous
than his creator.
So our best guess should be that the sentiment talk is cheap spread in its current form as a result of being associated with a long past literary phenomenon in Sam Slick, whose turn of phrase — perhaps even including talk is cheap — seemed to have delighted those over the pond.
Best Answer
The phrase 'cheap shot' in the literal sense of inexpensive "Projectiles (esp. balls or bullets, as distinguished from explosive ‘shells’) designed to be discharged from a firearm or cannon by the force of an explosive" (OED Online) does not appear in the sources I checked (free online popular news archives, Google Books, OED Online) until 1864:
(The Sydney Morning Herald, 18 Aug 1864.)
Earlier attestations of the phrase 'cheap shot' with reference to the action of shooting (a 'shot'), specifically in the sense of "9. a. An attempt to hit with a projectile discharged from a gun. ....", include two that draw on sense 9b, the figurative sense derived from 9a:
["shot, n.1". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/178651?redirectedFrom=cheap+shot (accessed September 21, 2016). Attested from 1841 as 'shot' and from 1973 as 'cheap shot'. Sense 14b refers to "a cannonball".]
Elsewhere than in OED Online, 'cheap shot' is defined more generally to include actions as well as remarks. Such definitions more accurately reflect the range of figurative senses I am familiar with:
(Random House Kernerman Webster’s College Dictionary. S.v. "cheap shot." Retrieved September 21 2016 from http://www.thefreedictionary.com/cheap+shot.)
The sense of 'cheap' in the phrase, overall, is the figurative
["cheap, adj., adv., and n.2". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/31047?rskey=CShTCr&result=2&isAdvanced=false (accessed September 21, 2016).]
That figurative sense of 'cheap' is often used disparagingly.
The first of the two early attestations may be interpreted as a literal reference to the two dollars spent for a shot that killed forty-seven ducks. However, the decades-long series of elaborations and reproductions of the story, in works such as More puniana; or, Thoughts wise and otherwhy's, 1875, suggest otherwise.
(Family Herald, Volume 2, 1844, a British publication, as reproduced in South Australian Register, 4 Oct 1845.)
The second early attestation of the phrase, a 1918 use in figurative sense 9b, is quite evidently an elaborate pun:
(The Adelaide Chronicle, 27 Jul 1918.)
Chronologically between those two early attestations of the figurative sense 9b in anecdotal puns is this rather more prosaic 1896 use of the term in another British publication. Here the sense of 'cheap' is literal ('inexpensive') and the use of 'shot' is figurative:
(The Sketch: A Journal of Art and Actuality, Volume 12, 1896.)
Hard on the heels of the 1844 and 1918 uses of the term in figurative sense 9b comes a third such use, a slanted 1921 Australian use in a political context pertaining to religosity:
(The Freeman's Journal, Sydney, 24 Nov 1921.)
Later, in 1929, a use with reference to sports (hockey) appears. In this use, 'shot' has the extended literal sense of an 'attempt to hit with a projectile' (the goal with the hockey puck), while 'cheap' has the extended figurative sense of 'easily obtained' used somewhat disparagingly:
(The Heights, Boston College, 29 Jan 1929.)
Aside from uses in political contexts with disparaging reference to remarks in debates (Parliamentary Debates (Hansard): House of Commons Official Report, Volume 384, 1941), the next use I discovered was also a reference to sports—this time cricket:
(The Cairns Post, Queensland, 31 Dec 1947.)
The sense of that use is somewhat opaque to me, unfamiliar as I am with cricket jargon, but I surmise the use may be a more or less literal reference to 'shot' in the sense given earlier (9a), preceded by a figurative reference to 'cheap'.
Following the 120 year history of development shown above, uses with reference to professional US football and boxing began to make appearances in the 1960s. In these uses, the 'shot' is with a human body employed as a projectile, and the cheapness lies in the unexpected or sneaky nature of the hit. Along with those uses are others pertaining to discreditable actions and remarks:
(Limitation of Attorneys' Fees: Hearing, Eighty-ninth Congress, Second Session, 28 Feb 1966.)
(Film Culture, 1966.)
(The Running Back: A Novel of Professional Football, Hamilton Maule, 1966.)
(The realm of sport, 1966.)
(Review of Existential Psychology and Psychiatry, 1967.)
(Time, 1967.)
(Football Lingo, Zander Hollander, Paul Lionel Zimmerman, 1967.)
In summary, the term 'cheap shot' has been in use with the meaning
since 1844.
In later years, along with its other uses, the term came to be employed in sports, especially professional US football, where its meaning was applied to sport-specific actions and situations.