A brief glimpse at the OED “Etymology” section for the word “organ” reveals that it is an entire paragraph long. The gist of this section is that multiple definitions of the term have been borrowed from different languages at different times, but that it probably mostly comes from classical Latin and old French, and that its first English usage was in a now-obsolete sense, referring in early Old English to “various ancient musical, esp. wind, instruments. Chiefly in translations of, or allusions to, Scripture”.
That said, there are a couple key definitions of “organ” – of the many on the OED (fourteen as a noun, two as a verb, not including compound phrases or derivative words) – that are relevant to its uses in Ulysses. The first, derived from the ancestral Old English use of the word, is “a musical instrument (usually large) consisting of a number of pipes” – the church instrument that Bloom hears and thinks about in “Hades”, for example.
Organ, however, also takes on various less divine definitions, in its most neutral form simply referring to a kind of implement, OED definition 5a: “A means of action or operation, an instrument; (now) esp. a person, body of people, or thing by which some purpose is carried out or some function is performed.”
In Episode 7, however, we see a more specific branch of this definition, the periodical that is the organ of its cause, 5c: “A means or medium of communication, or of expression of opinion; esp. a periodical which serves as the mouthpiece of a particular political party, cause, movement, etc.”
The book’s first use of “organ”, however, referring to Bloom’s hunger for innards, refers to definition 7a: “A part of an animal or plant body that serves a particular physiological function (as the heart, liver, etc.).” This comes from the idea of the internal organ as a specified instrument within the body, with its first cited quote in the OED coming from 1425. Given Molly’s profession as a concert singer, it may also be important to keep in mind definition 8 in the OED: “The human organs of speech; the human voice.”
Given Joyce, of course, it’d be foolish not to consider definition 10, a euphemism at least as old as 1853: “The penis.” That an instrument common in churches could share the same word as one’s genitals surely must not have escaped Joyce’s notice.
Beyond just “organ” in its strict sense – the other definitions of which I won’t go into here, for brevity’s sake – there is also the related verb “organize,” which has taken on a meaning all its own despite differing only in the addition of a suffix: “to arrange into a structured whole” or, in the political sense “to put into place an administrative structure.” Thus the concept of the “organ” becomes an ideal of structure and administration, perhaps most closely associated with definition 5a, as an implement.
