Who are "Eleh" who could not prove their lineage?
Rashi: The Kohanim mentioned here (verse 61).
Ibn Ezra #2: Bnei Yedayah mentioned above (36). This Perush is primary.
Malbim: Kohanim from Bnei Chavayah Bnei ha'Kotz. They married Bnos Barzilai, and were called Bnei Barzilai. Also Yisraelim of paternal descent from Barzilai were called so! The former had no documents proving that they were Kohanim.
What was not found?
Rashi, Ibn Ezra #1: They could not find documents of their lineage.
Ibn Ezra #2: Bnei Yedayah (36) were not found in the document of their lineage.
Malbim: Each family used to have a document of lineage for the entire family, and each individual had a document of his own lineage. Neither was found.
"Kesavam" is singular (their document). Why is the verb plural (Nimtza'u)?
Ibn Ezra #1: Nimtza'u is plural because it pertains to many people. This is like "Tikrenah Milchamah" (Milchamah is singular; Tikrenah is plural, for we (Rabim) will encounter war).
Ibn Ezra #2: Really, Nimtza'u applies to Bnei Yedayah (36).
Malbim: The singular hints to the document for the family. The plural hints to individual's documents (refer to 2:62:2:3).
What is the meaning of "va'Ygo'alu"?
Rashi: They were Megu'al (sullied and repulsed) from Kehunah. They could not serve.
Ibn Ezra #1: They were Megu'al (with an Aleph - despised) from Kehunah.
Ibn Ezra #2: They were Megu'al (with an Ayin -purged) from Kehunah. The Aleph in "va'Ygo'alu" is in place of an Ayin.
Malbim: It was not known if Bnei Barzilai were Kohanim. This led to another Safek - due to this, they were not careful to marry girls Kesheros to Kehunah, and some fathered Chalalim.
