Gemara

(Mishnah): If one was on his way to a Mitzvah, e.g. Seudas Eirusin in his father-in-law's house...

(Beraisa - R. Shimon): A Chacham may not benefit from any meal that is not a Mitzvah.

(R. Yochanan): An example is a meal for the marriage of a Bas Kohen to a Yisrael or a Chacham's daughter to an Am ha'Aretz (ignoramus).

Bava Kama 80a: Rav, Shmuel and R. Asi went to Shevu'ah ha'Ben. Some say that it was Yeshu'ah ha'Ben.

Chulin 7b: Rebbi offered to host R. Pinchas ben Ya'ir for a meal.

R. Pinchas ben Ya'ir: I consent! Don't think that I vowed not to eat from Yisrael.

95b: Rav would not eat at a Seudas Reshus.

Rishonim

Mordechai (604, 605): A Chacham may not benefit from Seudas Reshus. Why may we eat a Seudas Nisu'in of a Bas Kohen or Bas Talmid Chacham to an Am ha'Aretz? Rabbeinu Meir answered that this is why the custom is to sing Zemiros and praises of the Chesed that Hash-m did with Adam and Chavah. Seudas Reshus is only if there is no Mitzvah, e.g. for camaraderie or big Seudos on Chanukah.

Terumas ha'Deshen (269): The custom is to make a Seudah to publicize Pidyon ha'Ben. This is like Rashi says (Bava Kama 80a). We must say that it is a Seudas Mitzvah, for Rav never ate at Seudas Reshus.

Poskim

Rema (OC 670:2): Some say that there is a small Mitzvah to have big Seudos during Chanukah. If there are Zemiros and praises [of Hash-m], it is a Seudas Mitzvah.

Magen Avraham (4): Likewise, if a Bas Talmid Chacham marries an Am ha'Aretz, if there are Zemiros it is a Seudas Mitzvah.

Question (Machatzis ha'Shekel 415:1): Why does this make it a Seudas Mitzvah? One could say the Zemiros and praises in his house. It need not be with the Chasan!

Answer (Kaf ha'Chayim 415:4): At the time of Seudas Nisu'in, one also rejoices the Chasan.

Shulchan Aruch (415:1): We make Eruv Techumim only for a Mitzvah, e.g. to go to... a drinking house or Nisu'in... and similar matters.

Magen Avraham (1): If a Bas Kohen or Bas Talmid Chacham marries an Am ha'Aretz, this is not a Mitzvah, like it says in Pesachim.

Gra (DH Shel): Seudas Erusin is a Mitzvah only for the Chasan, like it says "by his father-in-law."

Kaf ha'Chayim (2): Many hold that it is Seudas Mitzvah for everyone. One may be lenient like them.

Yam Shel Shlomo (Bava Kama 7:37): Shevu'ah ha'Ben is after a week passed, i.e. Bris Milah. Rashi explains that Yeshu'ah ha'Ben is Pidyon ha'Ben. Tosfos says that it is a celebration that the child was saved. It was the custom to make a Seudah. Both are proper Perushim. Rav would not eat at a Seudas Reshus. Granted, Seudas Bris Milah is Simchas Mitzvah, just like Seudas Chasan. However, Seudas Pidyon ha'Ben is not an explicit Mitzvah! Rather, any Seudah that is not in the way of camaraderie and Simchah, rather, in order to praise Hash-m or publicize a Mitzvah or miracle is called Seudas Mitzvah. Pidyon ha'Ben is to publicize the Mitzvah. According to Tosfos, it was to publicize the miracle. Seudos during Chanukah are Seudos Mitzvah, unlike the Rema, for they are to thank and praise Hash-m, and not for drinking and Simchah. The custom to eat cheese publicizes the miracle through which Yochanan's daughter killed the Yevani leader. Also Seudas Siyum is a Seudas Mitzvah. Abaye said that he would make a Yom Tov for Rabanan when a Talmid finished a Maseches (Shabbos 118b). Seudas Chinuch ha'Bayis is only for friendship, especially the way it is done nowadays. If one with Yir'as Shamayim wants to found his house with Torah and Mitzvos, and praises of Hash-m with Divrei Torah, it is a Seudas Mitzvah. Seudas Bar Mitzvah is the ultimate Seudas Mitzvah. Rav Yosef (who was blind) would have made a Yom Tov for Rabanan if he would have heard that he is obligated in Mitzvos [even though he is blind]. However, people make the Seudah on the day he turns 13, even though perhaps he did not yet bring two hairs. In any case, the boy expounds, so it is a Seudas Mitzvah.

Chavos Ya'ir (70): The Mordechai wrote that Seudos Chanukah are not Seudos Mitzvah, but Hagahos Mordechai wrote that they are Seudas Mitzvah, for they say Zemiros and praises. Also, one may not fast during Chanukah. This is a weak reason, for it suffices to taste one fruit a day [to avoid the Isur of fasting]! The Maharshal gave proper reasons why the Seudah of Bris Milah or Pidyon ha'Ben is Seudas Mitzvah, but there is no proof from Rav. Perhaps he went merely for dearness of the Mitzvah, to show how to do it, or hear the Berachah, but he did not eat. (I have seen Gedolim do so.) If any engagement in Torah makes a Seudas Mitzvah, there is no question why Rav went. The custom is to sing Ma'oz Tzur before a Seudah on Chanukah, so this does not make it a Seudas Mitzvah. Maharam taught that Zemiros and praises make a Seudas Nisu'in into a Seudas Mitzvah, i.e. for a Bas Kohen to an Am ha'Aretz. Sheva Berachos are not enough, for they are after Birkas ha'Mazon. If the Chasan and Kalah have the same status, it is a Seudas Mitzvah. I say that nowadays we do not have the Am ha'Aretz that Chazal discussed (49b). Every Nisu'in is the biggest Seudas Mitzvah there is. I am unsure about Shabbos night before the Milah and Nisu'in, and Seudas Eirusin and Chinuch Bayis. R. Shimon forbids a Chacham to benefit from any meal that is not a Mitzvah. Divrei Torah of a Chacham make a Seudas Mitzvah, so the only Seudas Reshus is a Bas Kohen to a Yisrael or a Bas Chacham to an Am ha'Aretz. R. Elazar declined invitations to eat at the Nasi's house, for it was Seudas Reshus. R. Zeira accepted invitations (Chulin 44b). Divrei Torah is not enough to make it a Seudas Mitzvah regarding a vow [not to eat from Seudas Reshus]. R. Pinchas ben Ya'ir told Rebbi 'don't think that I vowed not to eat from Yisrael. Why would Rebbi think so? He should assume that he does not eat a Seudas Reshus! I answer that surely when two great Chachamim eat, it is not Seudas Reshus at all. Rav's stringency, or anyone who accepts to do so, is only to eat with others the way people gather. It is common to have idle words, frivolity, lightheadedness and influence of wine.

Mishnah Berurah (2): Also Seudas Eirusin, or the Seudah of Kinyan that is customary to make nowadays, is a Seudas Mitzvah. Chavos Ya'ir says that nowadays we do not have the Am ha'Aretz that Chazal discussed [unless we know that he disgraces Mitzvos. He is no better than the Am ha'Aretz of the Gemara.] Surely a Bas Am ha'Aretz with an Am ha'Aretz is a Seudas Mitzvah. However, if we know that they will act improperly, e.g. mixed dancing, surely there is no Mitzvah to go, unless he will be able to prevent them from doing so.

Shulchan Aruch (640:6): Seudas Bris Milah, and the meal they make near the Yoledes, must be in the Sukah.

Magen Avraham (13): Maharik says that this is only a custom. It is unlike Seudas Chasan, which is a great Mitzvah. I.e. even though it is Seudas Mitzvah (YD 265:12), it is not such a Seudas Mitzvah, for it is not explicit in the Gemara. Therefore, 10 men suffice. Nachalas Shivah says that the Seudah the night before the Milah, to which we invite the Mohel, Sandek and other relatives and friends, is a Seudas Mitzvah regarding a vow [only to eat at a Seudas Mitzvah]. I prove otherwise from Maharam Mintz (109(43)). He says that the Seudah the night before Nisu'in is a Seudas Mitzvah only if the Chasan sends gifts. All the more so, the Seudah the night before the Milah is not Seudas Mitzvah.

Gra: It must be in the Sukah, for it is not a Torah Mitzvah like Nisu'in, to override Sukah. Also, there is no Chiyuv Simchah, like there is regarding Nisu'in.

Bi'ur Halachah (DH v'Seudas): The Magen Avraham connotes that if the Sukah cannot hold 10 people, one may eat in the house. However, the Gra says that it is not a Torah Mitzvah, so it never overrides Sukah. Surely, Seudas Eirusin, Pidyon ha'Ben, Bar Mitzvah, Siyum, etc. must be in a Sukah.

Shulchan Aruch (568:2): If one vowed to fast 10 days when he wants, and began fasting, and he needed to eat for a Devar Mitzvah, he may borrow the fast and repay later.

Magen Avraham (5): E.g. he needed to eat a Seudas Mitzvah that pertains to him. In any case he must fast a little longer than he usually does (Terumas ha'Deshen 271). However, he brings that Or Zaru'a permits even a meal for camaraderie. See 551:10. (Those who do not eat meat in the week of Tish'ah b'Av, or from Rosh Chodesh Av or Tamuz 17, may eat at a Seudas Mitzvah, e.g. Bris Milah, Pidyon ha'Ben, Siyum or Eirusin. Only those relevant may eat. In the week of Tish'ah b'Av, only 10 should eat.)

Kaf ha'Chayim (23): Also Seudas Siyum is permitted.

Magen Avraham (5): Therefore, I am lenient about a Seudas Mitzvah even if it does not pertain to him. Be'er Sheva says that Seudas Chanukas ha'Bayis is a Mitzvah in Eretz Yisrael, but not in Chutz la'Aretz. Benefit from a Seudah with a Chacham is like enjoying the radiance of the Shechinah (Berachos 64a).

Kaf ha'Chayim (26): The Magen Avraham connotes that a Seudah with a Chacham is a Seudas Mitzvah, unlike Chavos Ya'ir.

Rema: If a Bris Milah occurred during the fasts people normally have for BaHaB (Monday, Thursday and Monday after Tishrei and Nisan) or 10 days of Teshuvah, it is a Mitzvah to eat. He need not annul his vow. It is not customary to fast in such a case.

Magen Avraham (9): The same applies to Pidyon ha'Ben or another Seudas Mitzvah.

Rema (YD 178:3): In some places, they set a table with food on the night before Bris Milah. This is forbidden due to "ha'Orchim l'Gad Shulchan."

Shach (6): The Isur is only to set a table to leave the food on it. The custom to make a Seudah the night before is fine.