slang for "penis," 1939 (in James Joyce), according to OED and DAS from pudding (q.v.) in the same slang sense (1719), an extended use from the original "sausage" meaning of that word.
"hand, paw, fist," 1650s, "a nursery word," according to OED. It has been compared to Dutch poot "paw;" see paw (n.).
Entries linking to pud
c. 1300, paue, "hand or foot of an animal which has nails or claws" (distinguished from a hoof), from Old French powe, poue, poe "paw, fist," a word of uncertain origin. OED points to Germanic cognates and suggests a Frankish origin for the French word. Barnhart says evidence points to the Germanic word being borrowed from a Gallo-Roman root form *pauta (source also of Provençal pauta, Catalan pota). Century Dictionary says the modern Welsh and Breton words are from English and French. Compare patten. In reference to the human hand, especially if large or coarse, c. 1600.
c. 1300, "a kind of sausage: the stomach or one of the entrails of a pig, sheep, etc., stuffed with minced meat, suet, blood, and seasoning, boiled and kept till needed," perhaps from a West Germanic stem *pud- "to swell" (source also of Old English puduc "a wen," Westphalian dialect puddek "lump, pudding," Low German pudde-wurst "black pudding," English dialectal pod "belly;" also see pudgy).
The other possibility is the traditional one [also in Middle English Compendium] that it is from Old French boudin "sausage," from Vulgar Latin *botellinus, from Latin botellus "sausage" (the proposed change of French b- to English p- presents difficulties, but compare purse (n.)).
The sense of "dish consisting of flour, milk, eggs, etc., originally boiled in a bag until semi-hard, often enriched with raisins or other fruit" had emerged by 1670, from extension to other foods boiled or steamed in a bag or sack (16c.). German pudding, French pouding, Swedish pudding, Irish putog are from English. Pudding-pie as a type of pastry, especially one with meat baked in it, is attested from 1590s.
also podgy, "fat and short; thick, fleshy," 1824, from colloquial pudge "anything short and thick" + -y (2). Perhaps related to pudsy "plump" (1754), possibly a diminutive of nursery word pud (n.2) "hand, forepaw" (from mid-17c.). A connection with pudding (q.v.) also has been conjectured. In late 19c. it often appears on lists of English local or dialectal words; sources also mention puddy, punchy, pluggy, pudget as relatives or variants. Related: Pudginess.