"[In] any way, shape, or form" is a rhetorical idiom, in which shape and form tend to function as intensifiers. It is normally used for emphasis where the non-idiomatic phrases "[in] any way" or "[in] any form" would have been sufficient, and perhaps clearer. It is reliably attested at least as far back as 1826 (Colonial Times), already as a fully-formed idiom. Since this source is a provincial newspaper that can hardly have been responsible for popularizing the phrase, it must already have been in use before that time. However, I could not find any discussion whatsoever regarding its origins.
Earlier examples are found (around the 1790s) of the phrase in any shape, having much the same meaning, in both British and American usage (Mornington; Washington). However, this seems to have disappeared in later usage and been supplanted by the modern three-term form, which may have originated about 1800. Examples of both phrases are found during the 19th century, but afterwards most further usage of in any shape by itself seems either to mean a literal shape, or the sense of shape meaning condition, e.g. "not in any shape to/for [...]". Etymonline suggests (Etymonline) that the latter arose about 1865 in AmE, and so cannot have influenced the earlier usage. Thus it seems that the inclusion of shape in the idiom may have been motivated by the existence of the phrase in any shape, using a sense of the word that was seemingly current in the 18th century but had become obsolete by the 20th.
No dictionaries that I consulted included any clear description or origin for the modern idiom, only mentioning that it is indeed an idiom and offering usage examples. I also could not find any detail about the sense of shape employed in the phrase in any shape: Webster notes in 1828 (Webster) a sense of shape meaning manner, but no further detail is given.
If one understands any way, shape, or form straightforwardly, its emphatic intent is seemingly obscured, rather than strengthened, by the inclusion of what appears to modern speakers as an inappropriate or irrelevant term. My impression is that shape, specifically, is seldom, if ever, appropriate in any current context in which this idiom is used. It could be argued that the emphasis now comes from the contrast between the modern meanings of the various alternatives offered, but if so, it would presumably be understood that at least one of them is usually contextually inappropriate and the phrase is a rather self-conscious cliché.
So, I would like to ask: when and how did this sense of shape originate, and what led it to be displaced by the modern idiom also including way and form? Was the resulting three-term phrase always an essential pleonasm, or are there any attested, or at least reasonably plausible, cases in which way, shape and form are simultaneously applicable without being redundant, in either their original or modern senses?
Colonial Times and Tasmanian Advertiser. Vol. 11, no. 528: Hobart Town, Tasmania. 16th June 1826. Print.
Richard Wellesley, 2nd Earl of Mornington. Letter to Henry Dundas, Fort St. George, 7th June 1799. In The Despatches, Minutes, and Correspondence, of the Marquess Wellesley, K. G.: During His Administration in India, Volume 2, Montgomery Martin, Ed. London: Wm. H. Allen. 35. Print.
George Washington. Letter to Mary Washington, Mount Vernon, 15th February 1787. In The Writings of George Washington from the Original Manuscript Sources 1745–1799, Volume 29, September 1, 1786–June 19, 1788, John C. Fitzpatrick, Ed. Washington, D.C.: Library of Congress, 1939. 160. Print.
Douglas Harper. "Shape", entry in Online Etymology Dictionary. Accessed 21st November 2015. Available: http://www.etymonline.com/index.php?term=shape
Noah Webster. "Shape", entry in An American Dictionary of the English Language. New Haven, Connecticut, 1828. Republished as Webster's Dictionary 1828 - Online Edition. Accessed 21st November 2015. Available: http://webstersdictionary1828.com/Dictionary/shape