Gemara

Beraisa: If a person ate Ke'ilis figs or drank honey or milk and entered the Mikdash, he is liable.

26b - Question: What is the source that one who is drunk may not Duchan (give Birkas Kohanim)?

Answer (R. Yehoshua ben Levi): Birkas Kohanim is written right after Nazir to teach that a Kohen who will Duchan may not drink wine, just like a Nazir.

Suggestion: Perhaps he may not eat grape skins, just like a Nazir!

Rejection (R. Yitzchak): "Leshares u'Levarech bi'Shmo" - just like a Kohen serving in the Mikdash may eat grape pits (only Shtuyei Yayin is forbidden), he may bless.

Kesuvos 10b - Rav: One who ate dates may not give Hora'ah.

Sanhedrin 42a: "Ul'Roznim Ei Shechar" - those (on the Sanhedrin) engaging in the secrets of the world should not become intoxicated.

Kerisus 13b - Beraisa - Suggestion: Perhaps one is Chayav Misah for Bi'as Mikdash after drinking any amount of wine, or grape juice!

Rejection: "V'Shechar" - one is liable only if it can Meshacher (intoxicate), i.e. a Revi'is of wine pressed at least 40 days ago. "Yayin" forbids entering the Mikdash after drinking any amount, even grape juice (but one is not liable)

R. Yehudah says, "Yayin" forbids one who drank wine from entering the Mikdash; "v'Shechar" includes other intoxicants;

The Torah wrote wine explicitly to teach that one is Chayav Misah (b'Yedei Shomayim) only for wine. Other intoxicants are forbidden only by a Lav.

R. Elazar says, we expound (as if it said) 'Yayin Al Tesht v'Shechar Al Tesht' - do not drink in an intoxicating way;

If he paused while drinking, or added any amount of water, he is exempt.

The Beraisa that obligates one who ate Ke'ilis Deveilah (pressed figs) or drank honey or milk and entered the Mikdash is like R. Yehudah. The Halachah follows R. Eliezer.

"...Ul'Havdil Bein ha'Kodesh... U'Vein ha'Tamei...ul'Horos" - the Isur also applies to ruling about Hekdeshos, Tum'ah and Taharah, and Hora'ah.

Rishonim

Rif and Rosh (Megilah 16a and 3:23): One who is drunk may not Duchan. Birkas Kohanim is written right after Parashas Nazir to teach that a Kohen who will Duchan may not drink wine, just like a Nazir.

Rambam (Hilchos Bi'as Makdish 1:3): Just like it is forbidden for a Kohen to enter the Mikdash while drunk, one may not give ruling while drunk - "(Yayin v'Shechar Al Tesht...) u'Lhoros". Even if one's mind was slightly befuddled due to eating dates or drinking milk he may not rule. However, he may rule about something so explicit in the Torah that even Tzedukim (who deny the oral tradition) know it, e.g. that blood is forbidden.

Rambam (Hilchos Tefilah 15:4): Wine disqualifies a Kohen from Birkas Kohanim. If he drank a Revi'is at once he may not Duchan until he sobers up, for Birkas Kohanim is equated to Avodah. If he paused in the middle or if the wine was diluted with water, he is permitted. If he drank more than a Revi'is, even if he paused and it was diluted he may not Duchan until he sobers up.

Question (Lechem Mishneh): The Rambam rules like R. Eliezer regarding Birkas Kohanim, but he forbids other intoxicants like R. Yehudah regarding Bi'as Makdish! Also, regarding Bi'as Makdish he rules like R. Eliezer regarding one who paused while drinking!

Answer (Lechem Mishneh): The Rambam holds that R. Eliezer does not argue with R. Yehudah. He merely adds to R. Yehudah's words.

Kesef Mishneh: The Hekesh between Avodah and Birkas Kohanim is a mere Asmachta. Therefore, only one who would be liable for Avodah, i.e. he drank wine in an intoxicating way, is forbidden to Duchan.

Rebuttal (Taz OC 128:36): There is no source to say that the Hekesh is only an Asmachta. Tosfos (Sotah 38a DH Harei) understands that it is mid'Oraisa. Therefore, other intoxicants forbid a Kohen to Duchan. Since we have a Shi'ur only for wine, a Kohen should not drink any amount of other intoxicants before Birkas Kohanim.

Question: Rav rules like R. Eliezer, who exempts for Bi'as Mikdash one who was drunk from other intoxicants. But Rav forbids one who ate dates from giving Hora'ah!

Answer #1 (Tosfos Kesuvos 10b DH Omar): R. Eliezer exempts for Bi'as Mikdash, but he agrees that it is forbidden mid'Oraisa.

Answer #2 (Lechem Mishneh): R. Eliezer is Mechayev for Bi'as Mikdash. He agrees with R. Yehudah's Drashah and adds to it.

Answer #3 (Tosfos Kerisus 13b DH Omar): Rav forbids Hora'ah mid'Rabanan.

Poskim

Rema: (YD 242:13): One must be careful not to give Hora'ah when he is drunk from wine or other intoxicants. This applies even to a simple matter, unless it is clear in the Poskim and everyone knows it.

Gra (28): Tosfos' question forced the Rambam to rule like R. Yehudah, even though the Halachah follows R. Eliezer.

Shulchan Aruch (OC 128:38): If one drank a Revi'is at once he may not Duchan. If he paused in the middle or some water was mixed in, he is permitted. If he drank more than a Revi'is, even if it was diluted and he paused several times he may not Duchan until he sobers up.

R. Yerucham (Toldos Adam v'Chavah 3:6, Sof 27:3): A drunk Kohen may not Duchan. It seems that this is only if he is as drunk as Lot (when he slept with his daughters).

Beis Yosef (DH Shikur): R. Yerucham equates Birkas Kohanim with Tefilah. This is wrong. The Gemara equates it to Avodah.

Magen Avraham (55): R. Yerucham refers to one who drank other intoxicants. He may not Duchan because he is exempt from Mitzvos like a lunatic.

Prishah (48 DH v'Gam): Tosfos in Kerisus says that mid'Rabanan, one who is drunk from other intoxicants may not give Hora'ah. It is logical that if one is so inebriated that he cannot speak in front of the king, Chachamim also forbid him to pray or Ducham, even if he is not drunk from wine. However, they did not forbid one who drank less than a Revi'is of other intoxicants to pray or Ducham. Surely Hora'ah is forbidden, just like one who ate dates. However, the Isur to pray or Duchan when drunk is only mid'Rabanan, so regarding other intoxicants it is forbidden only if he is totally drunk.

Mishnah Berurah (141): Many Acharonim hold that even from other intoxicants, if he is too drunk to speak in front of a king, he may not Duchan (just like he may not pray).

Kaf ha'Chayim (225): L'Chatchilah one should be stringent not to Duchan until he sobers up even from other intoxicants. B'Di'eved, if he already went up he does not go down.