Bentching can be recited in any language that you understand. To make it a “choice” mitzvah, bentch in Lashon Hakodesh. (ShA1 – MB1)
How Loud?
Just thinking the words – not yotzay
Enunciating without hearing yourself – yotzay b'dieved.
Loud enough to hear yourself – l’chatchila.
Out loud – extra good for kavana and as not to forget the additions for Shabbos and Rosh Chodesh. (ShA2 – MB2,3)
If for some reason you are unable to speak, at least think the words of Birkas Hamazon. However, if later the oness goes away before digestion begins, do not rely upon your “thinking– bentching” – bentch now properly. (MB2)
If you are intoxicated after the meal, you are still allowed to bentch. L’chatchila you should bentch before the point that you aren’t fit to speak in front of a king. (ShA4 – MB6) LAWS OF BIRKAS HAMAZON