Q. Until when can the family of a bar mitzva bochur make a seuda after the day he became of age?

A. Maharam Brisk (2: 68) and other Poskim maintain that the correct and best time for the bar mitzva seuda is on the day the bochur actually begins his obligation of keeping mitzvos (Bo Bayom).
Pischei Teshuva (Y.D. 217: 16) quotes Chavos Yoir that up to three days after the birthday one may still celebrate the seuda, since the imprint is retained and the impression still remains, as we similarly find in regards to the takonas Ezra of reading the Torah at least within three days.
However, many postpone and celebrate the main seuda on the Shabbos after, even when the Bo Bayom was at the beginning of the week, as they want to include the guest that may not be able to attend on a weekday. Nitei Gavriel (Bar Mitzva 16: 8) quotes Mogen Avrohom, Divrei Yatziv, et. al. And mentions that so was the tradition of the Chasam Sofer, Ksav Sofer and others).
Nonetheless, Poskim stress that the bar mitzva bochur should impart and say his drosho (traditional bar mitzva Torah-speech) at that occasion to ascertain it is a seudas mitzva. Maharam Brisk (ibid.) maintains that when the bochur has not yet learned properly his drosho, one may postpone the seuda until he is properly prepared.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a