Sitting during the recital of an after blessing:
The general rule
Birchas Hamazon: One is required to sit while reciting Birchas Hamazon. He may not stand or lay down. This applies irrelevant of the position in which one ate, whether he was walking in his home when he ate or he ate standing or laying down, nonetheless, when it comes time to Bentch, he must recite it while sitting. In the event that one did not sit during Birchas Hamazon, then he fulfills his obligation, even if he Bentched while walking.
Meiyn Shalosh: One is only required to recite Birchas Hamazon in a sitting position, while other [after] blessings are not required to be said sitting. However, some Poskim rule one is required to recite Meiyn Gimel [i.e. Al Hamichya/Peiros/Gefen] in a sitting position, just as Birchas Hamazon. Practically, one is to suspect for the latter opinion, and recite Meiyn Shalosh in a sitting position.
One is initially required to recite Birchas Hamazon in a sitting position, and should be stringent to also recite Meiyn Shalosh in a sitting position. If one recited the blessing in a standing position, he nevertheless fulfills his obligation. One is not required even initially to recite Borei Nefashos in a sitting position, [although some say it is proper to do so].
Until what part of Birchas Hamazon must one remain sitting?
Some Poskim rule one is required to sit for the entire duration of Birchas Hamazon, including the fourth blessing of Hatov Vehameitiv. One is to remain sitting even during the Harachamon’s, until after Oseh Shalom.
 Admur 183/12; Michaber 183/9; Rambam Hilchos Brachos 4/1; Brachos 51b
 The reason: As one is able to concentrate more while sitting. [Admur ibid; Michaber ibid] This is hinted to in the verse “Vesavata Uveirachta”, as Vesavata can be read as Vesheiv Eis, that one should sit and then Bentch. [Tosafus ibid in name of Rebbe Moshe Albert]
 The reason: One is not to Bentch in a laying position, as doing so is an act of arrogance, and rather he is to sit in awe. [Admur ibid]
 Admur ibid; Rama ibid; Mordechai Brachos 184; Rambam ibid
 Admur 183/13
 Stam opinion in Admur ibid; Tosafus Brachos 51b; See Biur Hagr”a who implies that all Rishonim who hold one is not required to recite Meiyn Shalosh in the original place of eating agree here as well that one is not required to sit while reciting it; Kaf Hachaim 184/50
The reason: As the Sages were only stringent regarding Birchas Hamazon, being it is a Biblical after blessing. [Admur ibid]
 2nd opinion in Admur ibid; Opinion in Michaber 183/10; Mordechai Brachos 184; Rambam Hilchos Brachos 4/1; See Biur Hagr”a who implies that all Rishonim who hold one is t required to recite Meiyn Shalosh in the original place of eating, agree here as well that one is required to sit while reciting it.
 The reason: Although Meiyn Shalosh is only a Rabbinical requirement, nonetheless, since it is similar to the three Biblical blessings, therefore it should be said in the same sitting position. [Admur ibid]
 Admur ibid; Chesed Lealafim 183/10; Ben Ish Chaiy Chukas 4; Kaf Hachaim 183/51
 Admur 183/13
 Chesed Lealafim 183/10; Ben Ish Chaiy Chukas 4; Kaf Hachaim 183/51; See P”M Pesicha Koleles Brachos; 432 M”Z 1
 M”B 183/31; See Shaar Hatziyon ibid for explanation; See Halach Berura [Yosef] ibid
 Ruach Chaim 191/2; Kaf Hachaim 191/5