How much alcohol does one need to consume in order to be halachically drunk or intoxicated?
A Kohen can't do any avoda or bless the Israelites after consuming a certain sum of wine. Another problem would be with giving someone punishment through a beis din (lashes, stoning, etc), and the defendant claims he was intoxicated when the witnesses warned him.
According to Daf Yomi - Yoma 49 - Drunk Kohen the shiur for drunkenness is only a reviis. While this appears to be well below the level that would make him obviously drunk, it does prevent him from duchening or a rav from giving a psak.
If he drinks wine more that a reviis (anywhere between 3.3 oz. and 4.6 approx), then he cannot duchan. This is if he drank this amount at one shot and he didn't drink water with it.
If he drinks other intoxicating liquids, then he can duchen as long as he is not drunk.
This is based on the Ramban as cited below.
The rationale of the Rambam is based on a Mishna in Bechoros that states that one who is שיכור is not allowed to do the avodah because it is considered a מום - a blemish and a blemish which is only applicable to a person and not an animal does not invalidate the korban. This explains why by ברכת כהנים, the Rambam only mentions wine for that is learned from the passuk - יין ושכר אל תשת, however a כהן who drinks other liquids and is rendered a בעל מום, he would still be permitted to דוכן.
As SabbaHillel said, that for Duchening, one would need to drink a Revi'is of wine.
The Gemara in Eiruvin 64a says:
אמר רב יהודה אמר שמואל שתה רביעית יין אל יורה However, Rav Naḥman did not give his approval to all of Rav Yehuda’s rulings, as Rav Yehuda said that Shmuel said: If one drank a quarter-log of wine, he may not issue a halakhic ruling,However, Rav Naḥman did not give his approval to all of Rav Yehuda’s rulings, as Rav Yehuda said that Shmuel said: If one drank a quarter-log of wine, he may not issue a halakhic ruling,
אמר רבה בר רב הונא שתוי אל יתפלל ואם התפלל תפלתו תפלה שיכור אל יתפלל ואם התפלל תפלתו תועבה
On the topic of drinking wine, Rabba bar Rav Huna said: One who has drunk wine must not pray, but if he nonetheless prayed, his prayer is a prayer, i.e., he has fulfilled his obligation. On the other hand, one who is intoxicated with wine must not pray, and if he prayed, his prayer is an abomination.
היכי דמי שתוי והיכי דמי שיכור The Gemara poses a question: What are the circumstances in which a person is considered one who has drunk wine; and what are the circumstances in which a person is considered one who is intoxicated with wine? (ibid)
פתח חד ואמר היכי דמי שתוי והיכי דמי שיכור שתוי כל שיכול לדבר לפני המלך שיכור כל שאינו יכול לדבר לפני המלך
One of them opened the discussion and said: What are the circumstances where a person is considered one who has drunk wine, and what are the circumstances where a person is considered one who is intoxicated with wine? One who has drunk wine refers to anyone who has drunk wine but whose mind remains clear enough that he is able to talk in the presence of a king. One who is intoxicated refers to anyone who is so disoriented by the wine he has drunk that he is not able to talk in the presence of a king.
(ibid.)
שיכור מקחו מקח וממכרו ממכר עבר עבירה שיש בה מיתה ממיתין אותו מלקות מלקין אותו כללו של דבר הרי הוא כפיקח לכל דבריו אלא שפטור מן התפלה
With regard to one who is intoxicated, his acquisition is a binding acquisition; that is, he cannot retract the transaction when he is sober, and similarly, his sale is a binding sale. Moreover, if he committed a transgression for which he is liable to receive the death penalty, he is executed; and if the offense is punishable by lashes, he is flogged. The principle is that he is like a sober person in all matters, except that he is exempt from prayer.
From Eiruvin 65a
