May one Daven Maariv or Bentch if he is drunk?
A. Blessings on foods:
All blessings over foods may be recited even if one is very drunk, to the point he cannot speak before a king.
B. Reciting Birchas Hamazon:
Initially one is to recite Birchas Hamazon prior to becoming drunk to the point that he cannot speak fluently before a King. If one did not do so, then [if he became satiated from the meal] he is to bentch even in a very drunk state.
C. Davening Maariv:
Is drunk to the point that cannot speak properly before a King: If one drank to the point that he is unable to speak in front of a king without slurring his words, then it is forbidden for him to Daven Shemoneh Esrei until he becomes sober. However, he may still recite Shema if he is able to speak fluently before the king, even if he can only do so with a slight slur. If however he is drunk to the point that he cannot talk fluently before a king, and he thus trips and stumbles on his words, then it is forbidden for him to recite even Shema. If the time of Davening has already passed by the time he is sober, then he is to Daven Tashlumin by the next prayer. One who went ahead and Davened in a state of total drunkenness has not fulfilled his obligation. Furthermore, his prayer is considered an abomination, and it is as if he has served idols. In such a case one is to Daven a second time upon becoming sober, and if necessary, makeup the prayer as Tashlumin.
Drank exactly a Revius or more but is not drunk: If one drank a Revius or more of wine, but has not reached the above state of drunkenness, then although he may Daven Shemoneh Esrei, he is to be careful to Daven inside a Siddur. If a Siddur is not available, then he is to delay Davening Shemoneh Esrei until he gets a Siddur. If the time of Davening will pass by the time a Siddur is available, then he is to Daven by heart.
It is only forbidden to Daven under the influence of alcohol if:
 Admur 99:1 and 185:5
 99:1; 185:5
 The reason: As blessings require only a minute amount of Kavana, which can be accomplished even when one is drunk, as one who is drunk is considered conscious of his activity for all matters, and is thus liable in all the punishments given in the Torah. This is unlike Shema and Shemoneh Esrei which require a much greater amount of Kavana, and one who is drunk cannot have such intense concentration, and his prayer is thus an abomination. [185:5]
 The reason: One may recite Birchas Hamazon according to all opinions if he is still able to speak fluently before a king, even if his words would slightly slur due to his drunken state. If, however, he is so drunk that he cannot speak before a king without stumbling on his words then it is disputed as to whether he is allowed to recite Birchas Hamazon in this state. Practically one is to avoid this dispute and recite Birchas Hamazon prior to reaching this state of drunkenness. [ibid]
 As this entire ruling of Admur ibid is in reference to a case that one is Biblically required to Bentch, and hence he rules Safek Deoraisa Lechumra. If however he was not satiated, in which case the requirement to Bentch is only Rabbinical [see Seder 2:1; 184:2], then he is not to do so as by a Rabbinical doubt we rule leniently.
 The reason: As Safek Deoraisa Lechumra. [ibid]
 Admur 99:1 regarding Shemoneh Esrei and 185:5 regarding Shema
 There are two levels of “properly” regarding this matter. 1) One who cannot talk without a slur, but can talk fluently without stumbling on his words. This is called Shasuiy. 2) One who cannot talk without stumbling on his words. This is called Shikur. [185:5] The state of Shikur is more stringent than the state of Shasuiy, as will be explained in this Halacha.
 185:5 defines this as Shasuiy
The reason: Admur ibid states that this matter [Shasuiy] is disputed between the two opinions regarding Birchas Hamazon. Admur ibid concludes to be stringent by Shema as Safek Deoraisa Lechumra.
 This is defined as “Shikur” in 185:5. This measurement is difficult to discern. The Makor Chayim 99:1 gives an alternative measurement: If one is unable to walk straight, then this is a sign that he is drunk to the point that it is forbidden for him to Daven or say Shema. [Brought in Piskeiy Teshuvos 99 footnote 17]
Admur ibid states that the above dispute by Shema is only in a case of “Shasuiy”, when one is still able to speak fluently with a slur in front of the king. However, when one is unable to speak in front of the king without stumbling on his words, this state is called Shikur, and in such a state all agree that it is forbidden for him to recite Shema and doing so is an abomination. This is because Shema and Shemoneh Esrei require a great amount of Kavana, and one who is drunk cannot have such intense concentration. [ibid]
 Meaning a state of “Shikur” as opposed to mere “Shasuiy”. [99:1]
The reason: This is derived from the response of Chana to Eili who charged her with praying in a drunken sate to which she responded [Shmuel 1:16] “Do not place your maidservant in front of an idol worshiper”. [ibid]
Consumed exactly a Reviis: One who drank exactly a Revius [86 ml.] of wine simultaneously, may not Daven until he sobers from the influence of the alcohol. This applies even if this will cause him to pass Zman Tefila. [99:1] It is possible to sober from the wine through taking a short nap, even momentarily, or through traveling a Mil’s distance [24 minutes of walking] either by foot or animal. [99:3]
Consumed more than a Revius: One who consumed more than a Revius of wine, which includes any amount over 86 ml, then even if one is still able to speak properly before a King, nevertheless he may not Daven until he is sober. [99:1] This can be accomplished either by taking a long nap or through traveling a distance of three Mil [72 minutes] by animal. In any event it is all dependents on the amount of wine consumed. Hence if one feels that he has become sober, he may Daven even if he did not sleep or walk 3 Mil. [99:3]
The Custom today: In today’s times, it is no longer accustomed to refrain from Davening after consuming a Revius of wine, as the wines of today are not as strong as the wines of the past. This especially applies if one Davens with a Siddur, in which case there is no need to worry that one may stumble on his words due to a little bit of alcohol. [99:4]