Rashi and Rashbam: Bearing in mind that 'Nezirah' means 'P'rishah' (separating), ¹ it is a warning to the Kohanim to keep away from the Kodshim of Yisrael when they (the Kohanim) are Tamei.

Seforno: It is a warning to the Kohanim to treat the Kodshim of Yisrael as full-fledged Kodshim, and not to think that, since they (the Kohanm) are on a higher level of Kedushah than the Yisrael, their Kodshim is not holy. ²

Zevachim, 15b: It teaches us that if a Zar performs the Avodah, his Avodah is desecrated. ³

Zevachim, 45a: It implies that not Chayav for bringing the Kodshim of Nochrim be'Tum'ah. ⁴

Zevachim 45b: To incorporate in the Din of Chilul.

Rashi #1: The phrases must be inverted, and "asher Heim Makdishim Li" follows "Veyinazru mi'Kodshei B'nei Yisrael".

Rashi #2 ¹ : It is coming to include the Kodshim of the Kohanim themselves in the prohibition.

Ramban #1: What the Pasuk is saying is that the Kohanim should not desecrate Hashem's Holy Name via the Kodshim of Yisrael, nor via the Kodshim that they themselves sanctify for Hashem.

Ramban #2 (citing the Sifra): "Veyinazru ... " - to render them Chayav for desecrating the Kodshim of Yisrael ² via Pigul, Nosar and Tum'ah; "asher heim Makdishin Li" - to include the Kohanim's own Korbanos.

Ramban #3 (According to Kabalah): 'They should not desecrate the Name with which Hashem is sanctified (Havayah) because His Name pervades in the Mikdash of Hashem.

Seforno: The Pasuk is saying that the Kohanim should not desecrate the name of the Hekdesh that Yisrael sanctify to Hashem.

Zevachim, 45b: It teaches us that Kodshim which are not Matir anything are also included in the Din of Chilul. ³