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קח את הלוים means, win them over with fine words: “Happy are ye that ye are privileged to be servants of the Omnipresent!” (cf. Rashi on Leviticus 8:2.)

קח את הלוים, "Take the Levites! etc." Rashi explains that the word "take!" means by means of words. Apparently Rashi means that Moses was to separate the Levites from the camps of the Israelites and make a separate camp for them seeing the Levites had to guard their ritual purity more than ordinary Israelites. The proof is to be found in the words וטהרת אותם, "and purify them!" Clearly what concerns the Torah at this point is the need for the Levites to maintain a state of ritual purity.

קח את הלוים, “take (aside) the Levites, etc.” According to Ibn Ezra the reason why this paragraph was written here is to teach us that whereas only Aaron would perform the kindling of the lights, there were many other functions connected with the Temple service in which the Levites could participate, thus lightening the burden of the priests. [My edition of the Ibn Ezra describes the Levites as having been scattered among all the tribes, and they were now to be concentrated in one area. The same supposedly applied to the other tribes, also. Ed.] Nachmanides writes that after the firstborn and the Levites had been counted, they lined up in front of Moses awaiting his instructions. They were presented with the wagons that the princes had donated ready to commence their diversified duties around the complex occupied by the Tabernacle. There was an immediate need to ritually purify the Levites, who previously had not needed to be especially concerned about this in their daily routines.

קח את הלוים מתוך בני ישראל, “take the Levites from among the Children of Israel, etc.” The paragraph dealing with the separation of the Levites was written immediately after that of the Menorah, as the former was the exclusive domain of the priests, whereas now the Torah prepares the Levites for assuming their duties. The next paragraph deals with the Passover as an historical commandment remembering the Exodus, a commandment involving every single Israelite. This is the meaning of 9,2: “The Israelites shall make the Passover.” You will observe therefore that these paragraphs have been arranged in a careful manner in a descending order of those to whom they apply, i.e. the Priest, the Levite, the Israelite. The reason that G’d had to say: “take the Levites from among etc., etc.,” was that until then they had been an integral part of the other tribes.

Take them with words of persuasion. [The Torah] does not mean to physically “take” them, in the sense of an acquisition and the bringing of something into one's domain. The Levites were not acquired and they were not brought into his domain. See Parshas Lech Lecha (16:3) Bereishis on the verse “Sorai, wife of Avrom, took.”

קח את הלוים, “take the Levites;” this line was said on the day that the Tabernacle had been erected; (Talmud, tractate Gittin 60) seeing that the laws pertaining to the Levites were recorded in writing on that day, as on that day they commenced the part of their service that involved their daily songs of praise. The paragraph was written in chronological order, and the two previous paragraphs, one of which commenced with הקרב את מטה לוי, (Numbers 3,6) and the other which commenced with the words: ואני הנה לקחתי את הלוים, (Numbers 3,12) these paragraphs referred to the position where the Levies encamped around the Tabernacle. After the Tabernacle had been erected and the positioning of the flags had been arranged and the lights of the menorah had been kindled, G-d (Moses) ordered the Levites to commence their daily service. The paragraph dealing with the Levites’ service was written next to that of the kindling of the lights in order to tell us that the priests were to busy themselves with that at the same time as when the Levites were performing their service. Apart from that they would assist the Levites in their service, [seeing they were Levites also. Ed.] (Ibn Ezra)

מתוך בני ישראל, “from among the Children of Israel.” Up until that time they had been part of the ordinary Israelites. (Ibn Ezra).