Siman 185
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א בִּרְכַּת הַמָּזוֹן נֶאֶמְרָה בְּכָל לָשׁוֹן.
1 Birkas Hamazon can be recited in any language
ב צָרִיךְ שֶׁיַּשְׁמִיעַ לְאָזְנָיו מַה שֶּׁמּוֹצִיא בִּשְׂפָתָיו; וְאִם לֹא הִשְׁמִיעַ לְאָזְנָיו יָצָא, וּבִלְבַד שֶׁיּוֹצִיא בִּשְׂפָתָיו.
2 One needs to hear what he is reciting but if he does not hear he has fulfilled his obligation as long as he articulated the words
ג יֵשׁ מִי שֶׁאוֹמֵר דְּבַעַל הַבַּיִת עִם בָּנָיו וְאִשְׁתּוֹ, צָרִיךְ לְבָרֵךְ בְּקוֹל רָם, כְּדֵי שֶׁיֵּצְאוּ בְּבִרְכָּתוֹ.
3 There is an opinion that that when a ba’al habayis is with his children and wife he must recite birkas hamazon out loud so they can discharge their obligation with his recitation
ד אֲפִלּוּ נִשְׁתַּכֵּר כָּל כָּךְ עַד שֶׁאֵינוֹ יָכוֹל לְדַבֵּר כָּרָאוּי, יָכוֹל לְבָרֵךְ בִּרְכַּת הַמָּזוֹן.
4 Even if one got significantly drunk to the point that the person is unable to properly speak, one is still able to bless the Birkat HaMazon.
ה וְאִם בֵּרַךְ וְהָיְתָה צוֹאָה כְּנֶגְדּוֹ, אוֹ שֶׁהָיָה שִׁכּוֹר (פי' לְגַמְרֵי), נִסְתַּפְּקוּ הַתּוֹסָפוֹת וְהָרֹא"שׁ אִם צָרִיךְ לַחֲזֹר וּלְבָרֵךְ; וּמִשּׁוּם מֵי רַגְלַיִם פְּשִׁיטָא שֶׁאֵינוֹ חוֹזֵר לְבָרֵךְ.
5 If one blessed the Birkat HaMazon and [found] that there was feces near him or that he had been drunk, Tosafos and Rabbi Asher ben Yehiel were unsure if one needed to go back and re-bless the Birkat HaMazon, but not for urine; for that, one need not re-bless Birkat HaMazon.