Gemara

(Beraisa - R. Yehudah): One who eats the Gid ha'Nasheh of a Tamei animal is lashed twice (two sets of lashes);

R. Shimon says, he is not lashed.

(Rava): R. Shimon holds that the Gid has no taste (so the Isur Tamei does not apply), and he holds that the Isur Gid does not apply to Tamei species.

Pesachim 21b (R. Avahu): Wherever the Torah says "Lo Yochal", it forbids eating and benefit, unless there is a source to permit benefit, like we find regarding Neveilah.

22a - Question (R. Yitzchak Nafcha): It says "Lo Yochlu Venei Yisrael Es Gid ha'Nasheh" (yet one may benefit from it)!

(Mishnah): One may send a thigh to a Nochri with the Gid ha'Nasheh inside.

Answer: R. Avahu holds that when the Torah permitted (to give a Neveilah to a Ger to eat, this permits benefit from (every edible part, including the Chelev and) the Gid.

Question: This is like the opinion that the Gid has taste. How can we answer for the opinion that it has no taste (R. Shimon, above)?

Answer: Indeed, R. Shimon forbids benefit from the Gid!

(Beraisa - R. Yehudah): One may benefit from the Gid ha'Nasheh;

R. Shimon forbids.

23b: R. Yosi holds that the verse that permits Hana'ah from a Neveilah does not permit benefit from the Chelev and Gid (which are forbidden to eat even in slaughtered animals). "Ye'aseh..." permits benefit from the Chelev;

Question: Does he forbid Hana'ah from the Gid?

Answer #1: Indeed, he forbids!

Answer #2: He permits it from a Kal va'Chomer. Eating Chelev is a Lav with Kares, yet one may benefit from it. Eating the Gid is only a Lav, all the more so one may benefit from it!

R. Shimon forbids Hana'ah. He refutes the Kal va'Chomer, for Chelev is totally permitted in Chayos.

R. Yosi learns the Kal va'Chomer regarding Behemos (so this is not a refutation). Chelev of Behemos is never permitted.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 8:14): One may benefit from the Gid ha'Nasheh.

Magid Mishneh: The Rambam rules like R. Yehudah, for the Halachah follows him against R. Shimon, especially here, since the Stam Mishnah is like R. Yehudah. Even though in Pesachim we say that the one who holds that Gidim have no taste, he forbids Hana'ah, and we hold that Gidim have no taste, the Ramban answered that there is no need to say so (that Hana'ah depends on taste. It is not really true.) We concluded that one may benefit from the Gid ha'Nasheh, even according to the opinion that Gidim have no taste. The Rambam holds like this. This is primary.

Tosfos (99b DH v'Hilchesa): Since we hold that Gidim have no taste, the Gid ha'Nasheh is Asur b'Hana'ah. Pesachim 22a says that the one who holds that Gidim have no taste, he forbids Hana'ah. When we dig out (the Gid ha'Nasheh and its Chelev), we sell the meat to Nochrim, even though the Gid is inside. This is not Hana'ah from the Gid, since the Nochri pays only for what has taste. However, one may not send a whole leg to a Nochri, for it is more honorable when it is whole. The Mishnah permits doing so. We establish the Mishnah unlike R. Shimon, who holds that Gidim have no taste, and it is Asur b'Hana'ah.

Tur (YD 65): The Nochri has (more) gratitude for the Gid (for the thigh looks much nicer when it is intact).

Rosh (7:17): The Rambam permits Hana'ah from the Gid ha'Nasheh. Chachmei Lunil disagreed, and forbade Hana'ah. Tana'im argue about this. The Halachah follows R. Shimon against R. Yehudah. (Yam Shel Shlomo 7:18 - If) the Halachah does not follow R. Avahu, we must say that the Gid is Asur b'Hana'ah, for we hold that Gidim have no taste, so we cannot say that the Gid was permitted with Neveilah. R. Yonah said that he has a proof from Pesachim that it is Asur b'Hana'ah. He did not write the proof. It seems that he holds that the Halachah follows R. Avahu. Seemingly, the Halachah follows Chizkiyah (who say that "Lo Yochal" does not forbid Hana'ah), for he was the Rebbi of R. Yochanan, and the Halachah always follows him against R. Yochanan, and all the more so against R. Avahu, the Talmid of R. Yochanan.

Rosh: Also the Rif in Pesachim brought only Chizkiyah's opinion. On 23a, the Gemara suggested that R. Yosi ha'Glili and R. Akiva argue like R. Avahu and Chizkiyah. It rejected this, and said that all hold like R. Avahu. This is because it could not say that all hold like Chizkiyah, since R. Yosi ha'Glili needed a verse to permit Hana'ah from Chelev. Another proof that the Halachah follows Chizkiyah is that the Gemara concluded that he and R. Avahu argue about whether the Torah forbids Chulin b'Azarah. We hold that the Torah forbids it, like Chizkiyah. The Gemara asked a contradiction in R. Shimon regarding Chulin b'Azarah, and answered that he permits (only) when the animal was found to be Tereifah. This shows that all Tana'im forbid mid'Oraisa. In Chulin (85a), it is considered an improper Shechitah. R. Yehoshua ben Levi (Pesachim 23b) and R. Yochanan (Nazir 29a) forbid Chulin b'Azarah mid'Oraisa. In Ashkenaz they sell to Nochrim the Gid ha'Nasheh. In other lands they do not even feed it to a cat. Therefore I proved that one may benefit from it.

Yam Shel Shlomo (7:18): The Rambam rules like R. Avahu (8:15), and also that Chulin b'Azarah is mid'Rabanan. I proved that this is the Halachah. In any case, the Halachah follows R. Avahu. We rule that Shor ha'Niskal (an ox sentenced to be stoned) is Asur b'Hana'ah (Bava Kama 41a). The Sugya does not mention Chizkiyah.

Rashba (Toras ha'Bayis ha'Aruch 3:3 p. 82a): The Ramban wrote in a Teshuvah that the Gid is Mutar b'Hana'ah. The Gemara explicitly rules that Gidim have no taste. Firstly, the Halachah does not follow R. Elazar (in some texts, R. Avahu cited him) against Chizkiyah, the Rebbi of his Rebbi. The Stam Mishnah permits Hana'ah. R. Shimon argues in a Beraisa. We hold like the Stam Mishnah, like R. Yochanan, R. Elazar's Rebbi. The entire Sugya in Chulin permits Hana'ah. A Beraisa (94a) permits Hana'ah, and late Amora'im (Abaye, Rava and Rav Ashi) explain the Beraisa. No one mentions that R. Shimon disagrees. According to Chizkiyah, the Hana'ah does not depend on taste. He has no source to forbid Hana'ah, for the verse says "Lo Yochlu"! The Ramban said that even R. Elazar could say (that Hana'ah does not depend on taste), for we permit Hana'ah from a Kal va'Chomer from Chelev. The Gemara initially said that Hana'ah depends on taste, for we find that R. Shimon and R. Yehudah argue about both of these. The end of the Sugya shows that it does not depend on this. We do not reject our Stam Mishnah without a proof. The Gemara asked what R. Avahu and Chizkiyah argue about (l'Halachah), and it did not say that they argue about Gid ha'Nasheh. Also the Rambam permits.

Poskim

Shulchan Aruch (YD 65:10): One may benefit from the Gid ha'Nasheh.

Beis Yosef (DH v'Yesh): We cannot say that the Rambam permits Hana'ah for the Rosh's reason, for the Rambam (8:15) rules like R. Avahu! If so, he should have ruled that the Gid is Asur b'Hana'ah! We must say like the Magid Mishneh, that the Rambam holds that really, Hana'ah does not depend on taste. The Rashba (Toras ha'Bayis, and 1:210) says that some of his Rebbeyim forbid Hana'ah, and some permit. He holds like the latter, and says that this is the custom. However, the Zohar forbids, therefore it is good to be careful.

Note: In the Teshuvah, the Rashba said the custom is to forbid in his area, and some permit.

Darchei Moshe (12): There is no proof from the Zohar, since R. Shimon wrote the Zohar, but we rule like R. Yehudah against R. Shimon! The Beis Yosef himself said so in OC (25), and Isur v'Heter (21:4), that we sell the Gid ha'Nasheh to people who work with Gidim.

Bach (9): There is no proof from the Zohar, since that is R. Shimon's opinion. However, Semak forbids. It is proper to be careful about this.

Darchei Moshe (11): Isur v'Heter ha'Aruch (21:4) says that we permit Hana'ah because we hold that Gidim have taste. This is wrong. The Rosh refutes this. The Beis Yosef brings from the Rambam and Rashba that even though Gidim have no taste, it is Mutar b'Hana'ah.

Drishah (9): Even the stringent opinion permits selling a thigh to a Nochri, for he pays only for what has taste. However, one may not give a whole leg to a Nochri for a gift, like Tosfos says.

Gra (27): Even though we hold that Gidim have no taste, in the conclusion (Pesachim 23b), Hana'ah does not depend on this. Even R. Shimon permits, according to R. Avahu. The Halachah follows R. Yehudah against R. Shimon.