Gemara

Contradiction: It says "Pales Magal Raglecha v'Chol Devarecha Yikonu" (weigh which Mitzvah is best to do), and it says "Orach Chayim Pen Tefales Na'u Magloseha Lo Seda" (do any Mitzvah you can without concern for its magnitude)!

Answer: The first verse discusses a Mitzvah that can be done through others (you should do the biggest Mitzvah), the second discusses a Mitzvah that cannot be done through others.

Contradiction: It says "Yekarah Hi mi'Pninim v'Chol Chafetzecha Lo Yishvu Vah" (forego your desires, for they are less important than Torah, but not Hash-m's desires, i.e. Mitzvos), and it says "Ki Tovah Chachmah mi'Pninim v'Chol Chafatzim Lo Yishvu Vah" (forego even Mitzvos in order to learn)!

Answer: The first verse discusses a Mitzvah that cannot be done through others, the second discusses one that can.

Kidushin 40b - Question: Which is greater, Talmud Torah or doing Mitzvos?

Answer #1 (R. Tarfon): Doing Mitzvos is greater.

Answer #2 (R. Akiva): Learning Torah is greater.

(Rabanan): Learning Torah is greater, for learning leads one to do the Mitzvos.

Bava Kama 17a - (Beraisa - R. Nechemyah): "They honored (Chizkiyahu) in his death" - they put a Sefer Torah on his bed, and said that he fulfilled all that is written in it.

Question: Also we do that nowadays (surely, the verse discusses a greater honor)!

Answer (R. Yochanan): We even say that a person fulfilled the Torah, but we do not say that he taught Torah.

Question: But learning is great because it leads to fulfilling (this shows that fulfilling is greater)!

Answer: Fulfilling is greater than learning, but teaching is greater than fulfilling.

Megilah 3a - In Rebbi's house they abandoned learning Torah to hear the Megilah. They learned from a Kal va'Chomer:

We abandon Avodah to hear the Megilah. All the more so we abandon Torah to hear the Megilah!

Question: The Kal va'Chomer assumes that Avodah is greater than learning Torah, but this is not so!

R. Shmuel bar Uniya: The angel that rebuked Yehoshua came for Bitul Torah, not for Bitul Avodah. This shows that Torah is greater than Avodah.

Answer: Torah of the Tzibur is greater than Avodah, but an individual's Torah is not.

Beraisa: We abandon Torah for burial and to bring a bride to the Chupah.

Megilah 16b - (Rabah): Learning Torah is greater than honoring parents. Yakov was punished for 22 years that he was away, but not for the 14 years he learned in the house of Ever.

Pesachim 4a (Abaye): (Even) if a Chacham has a fixed time to learn at night, he should not begin to learn on the night of the 14th (before checking), lest he learn at length and miss checking (in the proper time).

Rishonim

Rif and Rosh (Pesachim 1b and 1:1): (Even) if a Chacham has a fixed time to learn at night, he should not begin to learn on the night of the 14th, lest he learn at length and miss checking.

Rambam (Hilchos Talmud Torah 3:3): There is no Mitzvah equal to Talmud Torah. Rather, Talmud Torah is equal to all the Mitzvos, because learning leads to fulfilling. Therefore, learning always comes before fulfilling.

Rambam (4): If one has an opportunity to do a Mitzvah or learn Torah, if someone else can do the Mitzvah he should not cease learning. If not, he should do the Mitzvah and resume learning.

Source #1 (Gra YD 246:45): We learn from Moed Katan 9b.

Source #2 (Migdal Oz): We learn from Kidushin 32b and 40b.

Source #3 (Yerushalmi Pesachim 24a, cited in Kesef Mishneh): R. Avahu sent his son to learn. He was upset to hear that he was engaging in Chesed, because Chachamim concluded that learning has precedence over Mitzvos. This is when someone else can do the Mitzvah. If not, the Mitzvah has precedence.

Rambam (Hilchos Chametz v'Matzah 2:3): We do not fix to teach Torah at the end of the 13th of Nisan. Similarly, a Chacham should not begin to learn at this time, lest he continue and not check at the beginning of the time.

Kesef Mishneh: The Rambam needed to forbid learning alone and b'Rabim, One might have thought that the concern lest the learning get drawn out applies only b'Rabim. Or, one might have thought that we are not concerned about a Rabim, for they will remind each other, or that Chachamim did not decree because it is like a Mitzvah that will be lost, for they will not gather again later.

Poskim

Shulchan Aruch (YD 240:13): Talmud Torah is greater than Kivud Av v'Em.

Pischei Teshuvah (8): This is only if one needs to leave the city to learn. If he is in the city he must serve his parents and then resume learning.

Shulchan Aruch (246:18): Talmud Torah is equal to all the Mitzvos. If one has an opportunity to do a Mitzvah or learn Torah, if someone else can do the Mitzvah he should not cease learning. If not, he should do the Mitzvah and resume learning.

Question (Kol Ben Levi, brought in Likutim in Frankel Rambam): The initial words of the Rambam (3:4), Tur and Shulchan Aruch (246:18) 'one has an opportunity to do a Mitzvah or learn Torah' suggest that he did not begin either yet. But if he had begun, one would not interrupt for another Mitzvah, even if no one else can do it. The Ran (Kidushin 13b DH Aba) says so about Kivud Av v'Em, and that this applies to all Mitzvos because one who is engaged in a Mitzvah is exempt from other Mitzvos. But the final words of the Rambam and Shulchan Aruch 'and resume learning' suggest that he already was learning!

Answer (Kol Ben Levi): For the Rambam and Tur we can say that there is no beginning regarding Torah, for each chapter, even every word, is a Mitzvah by itself. Therefore, even if one is learning, if a Mitzvah comes which no one else can do, he 'ceases' learning to do the Mitzvah, for it is as if he has not yet begun the next word of Torah.

Note: It seems that there are exceptions. We may not divide verses of the Torah (Megilah 22a). If one said half a verse, especially if it includes Hash-m's name, he must finish the verse. Rashi (Berachos 6b DH Agra d'Pirka) says that reward for learning (Torah she'Ba'al Peh) is only if one understands and remembers it so he can repeat it later. It seems that until this point he is in the middle of learning.

Or Yisrael (25, from Rav Zundel, the Rebbi of R. Yisrael Salanter): If one engages in a Mitzvah that cannot be done through others, such as Bikur Cholim or Chesed, it is considered as if he learned Torah, like it says in Moed Katan 9b and Shulchan Aruch (246:8).

Note: Presumably this should be 246:18. I did not find in our texts that it is considered as if he learned Torah, only that one is obligated to do the Mitzvah.

Shulchan Aruch (OC 431:2): One may not begin Melachah, or eat before Bedikas Chametz on the night of the 14th. Even if he has a fixed time to learn, he should not learn until checking. If he began to learn during the day he need not interrupt.

Beis Yosef (DH v'Kosav ha'Rav): R. Yonah infers that Abaye forbids beginning to learn at night before checking. The Tur disagrees, for the concerned lest he forget to check still applies. It seems that since this matter is mid'Rabanan, it suffices to be stringent not to begin learning then, but we need not interrupt one who began to learn b'Heter.

Taz (3): It seems that even R. Yonah is lenient only if the person learns a fixed amount every day. If not, he agrees that one must interrupt.

Taz (4): The Tur explains Abaye to teach that not only one who began learning beforehand must stop. Rather, even one who plans to learn a fixed amount and then check may not do so.

Rema: Some say that he must interrupt. This is the primary opinion.

Question: If one started learning before Kri'as Shma he need not interrupt. Why are we more stringent about Bedikah?

Answer #1 (Bach DH v'Kosav): Bedikah is less regular than Kri'as Shma, so we are concerned lest one forget to check.

Taz (2): Regarding Shma Chachamim were concerned only lest one miss the Mitzvah entirely, but regarding Bedikah they were concerned lest a person start after the proper time.

Answer #3 (Magen Avraham): Maharlbach (Hagahos Tur 3) says that Bedikah is more stringent because it is to prevent an Isur. I say that the Chiyuv to interrupt for Bedikah is only if he began b'Isur, in the half-hour before dark. The Beis Yosef says that Bedikah is not mid'Oraisa because Zman Bi'ur has not yet come.

Magen Avraham (5): The Isur is for one who learns in his house. People who learn Halachos in the Beis ha'Keneses are permitted. It seems that if they engage in deep investigation it is forbidden.

Magen Avraham (8): If one began to learn at night all agree that he must interrupt.