The early sources regarding the minhagim of Nittel and what some Jewish communities did on the night of Christmas, commonly mention that besides not learning Torah on that night, there was also a minhag to eat garlic (see Der judische The Theriak written by Shlomo Tzvi Hirsch in 1615. Also Neupolierter unf wohlgeschliffener Juden-Spiegel by Lothar Franz Fried from 1715. Also Samuel Friedrich Brenz quoted in Otzar Ha'Vikuchim.)Do any Jewish communities that keep Nittelnacht with regards to not learning Torah also have this minhag to eat specifically garlic on Nittelnacht?
The Nitei Gavriel Hilchos Chanukka page 412 writes that there are those who have a custom to eat garlic to ward off the evil since they need portection since they dont have their usual portection from Torah. He brings the source from the Siach Yitzchak siman 408,and its also brought by the Bais Yisrael 8:301 . See footnote 12 which brings another reason for eatimg garlic. The garlic will create such a strong smell that they will avoid tashmish.
- The first source you mention answers that.
See Kapitel 1 siman 20 here: It says that jews always had the custom to consume garlic in food, a fact that goes back to times of Torah (Bamidbar 11:5) and also the Talmudic times, but gentiles in some places didn't, so jews usually ate that in times in which they did not encounter gentiles, like jewish holidays or their holidays (aka, Nittle-Nacht).
Jews used to consume it all year but the christmas part was used for antisemitic purposes, as if it was made to mock christian faith and this may have spread through europe as something common and limited to those days. Perhaps some jews start to limit using garlic to certain periods of the year, but this was more a way to avoid the old antisemitic accusations (the “smelly Jew”) than a minhag with sources and all.
For more on this, see: Maria Diemling, 'As the Jews Like to Eat Garlick'. Garlic in Christian-Jewish Polemical Discourse in Early Modern Germany.
- With regards to not learning Torah part, it seems, also, have to do with avoiding (antisemitic) attacks in this particular time. On this, H.J. Zimmels writes as follows:
The real reason for the custom seems to be the following: in the Middle Ages the Jews used to be attacked on that night, therefore the Rabbis forbade their students to attend the house of study and no lectures were held. In the course of time, however, the reason was forgotten and only the custom remained.