In cities that were walled at the time of Yehoshua (notably, including Yerushalayim), Purim is celebrated on the fifteenth of Adar instead of the standard fourteenth. If the fifteenth falls on Shabbat, when some of the mitzvot of Purim are inappropriate, the various mitzvot of the day are spread over three days, which we call Purim Meshulash. We will start by explaining the concepts and then review the day-by-day activities. By the way, the fourteenth of Adar never falls on Shabbat.
Even in a Purim Meshulash, conceptually, the main day of Yerushalayim’s Purim is still the fifteenth of Adar, even though it is the least “eventful” of the days. Therefore, matters connected directly to tefilla and not problematic on Shabbat, are done on Shabbat. This includes reading the story of the battle of Amalek[1] as maftir, a special haftara, and saying Al HaNissim in Shemoneh Esrei and Birkat HaMazon.
Megillat Esther is not read on Shabbat for one of two reasons:[2] Rabbah says that it is out of concern that someone will carry the megilla in the public domain and thus desecrate Shabbat. Rav Yosef says it is because poor people look forward to receiving charity, which cannot be distributed on Shabbat, at the time of the megilla reading. As the rule is that Megillat Esther is never read after the fifteenth of Adar,[3] the reading is pushed up to Friday, the fourteenth of Adar. One should be extra careful to hear the megilla with a minyan in such a year,[4] since when the megilla is read early, it requires a minyan.
Matanot la’evyonim[5] follows suit, and the donations are given on the fourteenth of Adar.[6] After all, according to Rav Yosef, that was the whole reason to read the megilla early, and even Rabbah must accept some level of linkage between the megilla reading and matanot la’evyonim.[7]
According to most authorities, the se’uda[8] takes place on Sunday, the sixteenth of Adar.[9] The Yerushalmi[10] maintains that it is not held on Shabbat because it must be a se’uda whose obligation can be attributed only to Chazal’s decision at the time of Mordechai and Esther. On Shabbat, of course, there is a mitzva to have a festive meal irrespective of Purim, and so the Purim se’uda would remain indistinct. There are opinions that one can/should have a Purim meal on Shabbat and so some make an effort to have more food and wine than usual at the Shabbat-day meal.[11] At the Sunday meal, Al HaNissim is not recited, at least not in the body of Birkat HaMazon.[12]
The mitzva of mishlo’ach manot[13] is apparently linked to the Purim se’uda, and thus is performed on Sunday.[14] Those who want to have a Purim se’uda on Shabbat can attempt to fulfill mishlo’ach manot as well by giving food to a neighbor or having a guest at the meal.
Visitors to Yerushalayim over Shabbat (even if they celebrated Purim fully on Friday) are obligated (according to most authorities[15]) to do the mitzvot of both Shabbat and Sunday (wherever they are on Sunday) even if they leave Yerushalayim soon after Shabbat. This is because the obligations of Sunday are tashlumin (make-ups) for what ideally should have been done on Shabbat.[16] (One should give the mishlo’ach manot to someone who is obligated in the mitzvot of Sunday). Based on the same logic, one who comes to Yerushalayim after Shabbat is not obligated.[17]
Let us summarize by day: Friday- reading of the megilla and matanot la’evyonim; Shabbat- Al HaNissim and special maftir/haftara; Sunday- se’uda and mishlo’ach manot.