The article on Maoz Tzur in MyJewishLearning.com refers to an article by Ismar Schorsch, the former chancellor of the Jewish Theological Seminary, published in the journal Judaism in the fall of 1988, entitled "A Meditation on Maoz Zur." Schorsch's family escaped from Germany on the first day of Hanukkah of 1938, after his father had been freed (he had been arrested on Kristallnacht). He writes that his family always sang the first five stanzas of Maoz Tzur with great fervor during their Hanukkah celebration (p. 459): "The poem's theme of redemption seemed to offer a poignant comment on our family's experience." They omitted the sixth stanza, however.
He records the history of the poem as follows (p. 460): "In its present form, Maoz Zur consists of six stanzas. Since the days of Leopold Zunz, the first five have been ascribed to an unknown German poet named Mordecai, who lived sometime before the middle of the thirteenth century and whose name survives as an acrostic formed by the first letter of each stanza." Schorsch writes that the poem is written as if shortly after the Maccabees had retaken the Temple from the Syrian Greeks. "The rescue from 'Greek' tyranny triggers a recollection of earlier cases when God's intervention redirects the course of Jewish history." These are in Egypt, Babylonia, and Persia. The fifth stanza describes the "redemption at the time of the Hasmoneans."
The sixth stanza was composed later than the first five, and it is (p. 461) "an unabashed messianic plea for divine retribution upon Israel's Christian oppressors." He comments that it is often left untranslated in modern prayerbooks (like the Birnbaum siddur, which translates only the first five stanzas). The fifth stanza adds the final subjugator of the Jewish people - Edom (which in rabbinic interpretation is equated first with pagan and then with Christian Rome, thus becoming the code name for Christianity as a whole).
My rough translation (helped by Schorsch's discussion on p. 462):
Reveal your holy arm (cf. Isaiah 52:10) and bring near the day of salvation.This stanza is a more urgent request for divine salvation - rather than remembering the past salvation from danger and oppression at the hands of the Egyptians, Babylonians, Persians, and Greeks, it directly calls God to save his people from the Christians. Schorsch believes that this stanza was also written by an Ashkenazic Jew (p. 463), "stirred by the tremors and aftershocks of the Reformation," who believed that the Christian kingdom could only be overcome by direct divine intervention.
Avenge your servants against the evil kingdom.
The time has lengthened, and there is no end to the evil days.
Destroy the red one (Admon=Christianity) in the shadow of the cross,
and send forth the seven shepherds [Abraham, Isaac, Jacob, Moses, Aaron, Joseph, and David]
With this understanding of the meaning of the text, it's clear why Philip Birnbaum did not care to translate the stanza into English. Although he does not mention it in his entertaining introduction (full of jabs at earlier translations and editions of the prayerbook), he refrains from translating quite a number of potentially troublesome passages, particularly mystical ones, and in this case, one that could be viewed as an open attack upon Christianity, something that he presumably thought would be unwise even in the United States.