And as many as when they might not want to welcome you themselves, departing out from the community, that one, the dirt from those feet of yours? Knock off in witness against them.
There are two negatives in Greek, one referring to facts, another referring to choices and opinions. The negatives here indicate a choice that people make. There is also a rare word used here that has a double meaning, which, as typical of Christ's humor, ends the verse. See this article on the forms of Christ's humor. There is also a word missing in the KJV that makes an important point.
The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also") and, in a series, is best translated as "not only...but also."
The word translated as "whosoever" means "as great as", "as much as," and similar ideas of comparison.
There is an untranslated Greek word here meaning "if might" that indicates more of an expectation of something happening than "if" alone so "when" often works well in English.
The negative, "not," used here is the Greek negative of a subjective opinion. The sense is that "you don't want" to do something, not that it isn't done. If it wasn't done, the objective negative of fact would be used. More about the Greek negative in this article.
"Receive" is a Greek verb word, when applied to people as it does here, means "to welcome", "accept" or "to receive with hospitality". It is in a form of possibility ("might") where the subject doing this for or by themselves, "they might welcome you themselves". However, with the negative used, the sense is "they might not want to welcome you themselves".
The "you" here is plural, indicating all Christ's listeners.
There is no Greek word here meaning "when". It is added because the form of the verb "depart".
The word translated as "ye go out" means literally "to go or come out," but it has a secondary meaning of "making something come true." It is in the form of an adjective used as an adjective, "coming or going out".
The word translated as "of" means "from" in both location and when referring to a source.
The word translated as "that" is a word that means "that person there" "or "that one there". but it comes later in the phrase, after "city".
The Greek word for "city" meant not only a city but a nation, culture, or a society. It worked something like the word "community" today.
The word translated as "shake off" is a unique word for Christ to use. It is different than the common word used in the Matthew and Mark versions, which means "to shake out" while cleaning. This word means to "jostle from" as we would use "knock off" in English. Its is in the form of a command. The word comes after "dust" and "from your feet" making it work like a punchline.
The word translated as "dust" means a cloud of dust or dirt. It is also a metaphor for a dirty person. It is a rare word for Christ. This tends to indicate a double meaning.
The word translated as "from" means "from" in both location and when referring to a source.
The word translated as "feet" refers to human feet, birds's talons, and trampling things. Feet were the dirtiest part of the body and are still considered unclean in the Middle East.
The word translated as "for" means "into" a place, "towards" as a direction, and "up to" limits in time and measure. It means "for" in the sense of "for a purpose".
The Greek word for "testimony" means "testimony" and "proof."
The word translated as "against" means "against", "before", "during", "by" or "on."
The word translated as "them" is the Greek word commonly translated as pronouns in English, but it has a few shades of meaning our pronouns do not have. The word technically means "the same," and when used as a pronoun can mean "the true self" as opposed to appearances.
The word translated as "dust" also means a dirty fellow.
The "shake off" is a funny word appearing as a punch line.
καὶ (conj) "And" is from kai, which is the conjunction joining phrases and clauses, "and," or "but." After words implying sameness, "as" (the same opinion as you). Used in series, joins positive with negative "Not only...but also." Also used to give emphasis, "even", "also," and "just."
ἂν (particle) Untranslated is ean, which is a conditional particle (derived from ei (if)and an (might)) which makes reference to a time and experience in the future that introduces but does not determine an event.
μὴ (particle) "Not" is from me, which is the negative used in prohibitions and expressions of doubt meaning "not" and "no." As οὐ (ou) negates fact and statement; μή rejects, οὐ denies; μή is relative, οὐ absolute; μή subjective, οὐ objective.
δέχωνται (verb 3rd pl pres subj mp) "Will...receive" is from dechomai, which means "welcome", "accept," and "entertain" when applied to people and "take", "accept," and "receive" when applied to things.)
ἐξερχόμενοι (part pl pres mp masc nom) "When ye go out" is from exerchomai, which means "to come or go out of " "to march forth", "go out on", "to stand forth", "to exceed all bounds", "to come to an end", "to go out of office," and [of dreams or prophecies] "to come true."
τῆς πόλεως (noun sg fem gen) "City" is polis, which means "city", "citadel", "one's city", "one's country", "community", "state", "state affairs," and "civic duties." -- The Greek word for "city" meant not only a city but a nation, culture, or a society. It worked something like the word "community" today.
ἐκείνης (adj sg fem gen) "That" is from ekeinos (kakeinos), which means "the person there", "that person", "that thing," and, as an adverb, "in that case", "in that way", "at that place," and "in that manner."
τὸν κονιορτὸν [uncommon](noun sg masc acc) "The dust" is from koniortos, which means "dust raised or stirred up", "cloud of dust," and more generally,"dirt," or "sweepings," and, as a metaphor, "dirty fellow."
εἰς (prep) "For" is eis, which means "into (of place)," "up to (of time)", "until (of time)", "as much as (of measure or limit)", "as far as (of measure or limit)", "towards (to express relation)", "in regard to (to express relation)", "of an end or limit," and "for (of purpose or object)."
αὐτούς (adj pl masc acc) "Them" (adj sg masc acc) "Him" is autos, which means "the same," and the reflexive pronouns, "myself", "yourself", "himself", "herself", "itself," or the oblique case of the pronouns, "him", "her," and "it." It also means "one's true self," that is, "the soul" as opposed to the body and "of one's own accord."