Joshuan judges
[. . . He lived there . . .] before joshuan judges had given us numbers or Helviticus committed deuteronomy (one yeastyday he sternely struxk his tete in a tub for to watsch the future of his fates but ere he swiftly stook it out again, by the might of moses, the very wat- er was eviparated and all the guenneses had met their exodus so that ought to show you what a pentschanjeuchy chap he was!)
Continuing the theme of origins, the passage refers to early books of the Old Testament: joshuan judges = Joshua and Judges; Helveticus = Leviticus; guenneses = Genesis; also Numbers; Deuteronomy; and Exodus.
When he puts his head (tete) in the tub to wash his nose (watsch the future of his fate -- see entry), the water evaporates (eviparated = evaporate + separate + parted) like the Red Sea before Moses.
yeastyday: feast day + yesterday + yeast; unleavened bread is bread made without yeast. Passover, the feast of the unleavened bread, celebrates the events of Exodus (wherein is also described the parting of the Red Sea).
Helveticus: Like the Judeans, the Helvetii were a tribe conquered by the Romans.
There may be a further punning connection between "Helveticus" and the Jews: the word "jeu" (meaning play, toy, or game) in "pentschanjeuchy" is most often used by English-speakers in the phrase "jeu d'esprit"; the philosopher Helvetius is best known for the work "De L'esprit," an anti-religious work.
tub, sternely, swiftly: With that in mind, the adverbs "sternely" and "swiftly" refer to Lawrence Sterne and Jonathan Swift, both born in Ireland (Swift in Dublin). Swift wrote "A Tale of a Tub," an anti-religious work.
Sterne wrote "Tristram Shanty" -- the name "Tristram" occurs in Wake's opening lines.
pentschanjeuchy: Continuing in the biblical theme, a word play on the pentateuch, the first five books of the old testament. The character Punch (in Punch and Judy puppet shows) is noted for his long hooked nose; the name "Punch" may derive from "pou," as in "poultry," referring to a rooster's beak. (Joyce's spelling is hard to decode; it seems to combine the French words pents, change or chanson, and jeu, meaning think, change or song, and play/game/toy.)
"Punch and Judy" is British slang for "moody" -- here it could mean he is "hot-headed," in that sticking his head and/or nose in the water causes it to evaporate. (And moody might be a further pun on "muddy," like the floor of the Red Sea crossed by Moses, who would then be "a muddy chap.")