"Three questions on three verses in Isaiah (Is.21:4; 28:10, & 66:24)."
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Question #1:  

Could you tell me what the Lord is talking about in Isaiah 24:1?
Response #1:  

This verse is prophesying the Tribulation and using that far future event as an analogy for the Assyrian invasion: see Part 1 of the Coming Tribulation  (section IV.1.b., "The Day of the Lord Paradigm"). Here's what I write about this context in that study:
"During the Tribulation, these divine restraints upon the practice of evil will be removed as never before, so that mankind will serve the devil to an unprecedented degree, bringing down upon itself the unprecedented judgment of God. As a result, the Tribulation will be, truly, "the worst of times", for in it the most intense temporal judgment of God will be leveled upon the most egregious human behavior in history (cf. Mic.7:13): 
Behold, the Lord is about to empty the earth and lay it waste, and He will mar its face and scatter its inhabitants. And it will be the same for the people as for the priest; for the servant as for his masters; for the maidservant as for her mistress; for the buyer as for the seller; for the lender as for the borrower; for the creditor as for the debtor. The earth shall be thoroughly emptied and thoroughly plundered, for the Lord has pronounced this decree. The earth mourns; it wastes away. The world languishes; it wastes away. [Even] the celebrities of the earth languish. For the earth has befouled itself at the hands of its inhabitants. For they have transgressed the teachings [of God]; they have altered [His] statute[s]; they have violated the eternal covenant. Therefore a curse devours the earth, and its inhabitants are punished. Therefore the inhabitants of the earth are incinerated, and little of mankind remains.
Isaiah 24:1-6 " 
Note the emphasis above. In addition to ... 
1) the horrible things the earth will experience through the further degeneration of human behavior as a result of the removal of Holy Spirit restraint (cf. 2Thes.2:6-7; and see Part 2B of the Coming Tribulation series, where this issue is discussed in conjunction with the removal of the "seven seals"). 
and 
2) the horrible things the earth will experience as a result of the unprecedentedly bestial policies of antichrist and Satan's most direct administration of the world in its history ... 
... in addition to these two horrific trends, the Tribulation will also constitute the most intense period of divine judgment upon precisely these two egregious trends. For it is just as in the case of presumptuous individual sin, where we have natural consequences, and social consequences, and divine consequences. To give a crude analogy, a person involved in an armed robbery may 1) be injured by a gunshot in the attempt (natural consequence); 2) be caught, convicted and imprisoned for the act (social consequences), and further 3) be subject to the wrath of God for conceiving (mental), conspiring (verbal), and executing (manual) the crime - and those of us who rightly fear God understand that this last set of consequences, namely, those that come from the hand of God, are in truth the most terrifying of all, both temporally and eternally. In the analogy above, the actions of the world as a whole (the most significant of which from the divine point of view will be the Great Persecution of the Church and the unprecedented martyring of a great percentage of genuine believers then alive on earth during the Tribulation's second half) will rate the most intense discipline or divine judgment seen since the great flood. 
The tremendous mortality and physical devastation that results directly from the Lord as a response to world's unchecked evil (especially as expressed in persecuting and murdering His holy ones) is what is primarily in view here in Isaiah 24:1, although there is certainly a sense in which the suffering and devastation that arise from the first two causes discussed above is also not outside of the foreknowledge and will of God. The seven trumpet (warning) judgments, and the seven (punishment) bowl judgments in Revelation comprise the most notable installments of this "laying waste", encapsulated for us in the Isaiah quote. 
Yours in Him who is our only true Refuge, our Lord Jesus Christ. 
Bob L. 
Question #2:  

Could you tell me what Isaiah 28:10 means? 
Response #2:  

Although this a somewhat straightforward passage, it can be difficult to translate because of the problems involved in rendering the Hebrew here into English, and because of the complications caused by the fact that two following verses are quoted in the New Testament (1Cor.14:21 quotes verses 11-12). The best way to start is to give you my own translation of the broader context, Isaiah 28:8-13, which really must be considered as a unit (it consists of three stanzas, each introduced by the Hebrew conjunction chiy, literally "thus", and translated below as "and so it is that"): 
And so it is that all the tables are full of vomit and filthiness without any [clean] place, so to whom can He teach knowledge, and who will understand His message? These [people are like those just] weaned off milk, fresh from the breast (i.e., they have no deep spiritual understanding). 
And so it is that [they mock My message, saying] "Order upon order, order upon order. Command upon command, command upon command. The one is pointless, and so is the other". 
And so it is that with mocking lips and a strange tongue He will speak to this people, the very ones to whom He said [clearly] "This is the resting place; give rest to the weary!". For although this was [true] repose (i.e., for them to listen and obey), yet they were not willing [to do so]. Therefore the Word of the Lord will [likewise] become to them "Order upon order, order upon order. Command upon command, command upon command. The one is pointless, and so is the other", that they may go and fall backward, and be shattered, and caught, and captured.
Isaiah 28:8-13
This passage is a complaint and an accusation by the Lord through the hand of Isaiah against the apostasy of the Northern Kingdom (which was soon to be obliterated at the hands of the Assyrians for their rebellion and idolatry). God had of course given them every chance, earnestly sending out His message to them, but their response was to ridicule it - the Hebrew wording of their response (qav ve qav, qav ve qav, tsav ve tsav, tsav ve tsav etc.) is very sing-songy and has a clear quality of mockery (akin to "we played the pipes, you didn't dance; we played the dirge, you didn't mourn; Lk.7:32). The messages to the North were no doubt simplistic - but they had to be for people so far from God, so deep into apostasy, spiritual children, barely weaned. But instead of gratitude for His concern, instead of thanks and response to His earnest call for them to turn and enter His rest, they mocked Him, mocked His message (it's an old story, isn't it?). And so now they will reap what they have so imprudently sown, and the Word of God will really be just gibberish to them (qav ve qav, qav ve qav, tsav ve tsav, tsav ve tsav etc.), like parables which are not understood (cf. Matt.13:10-15). For this message did in fact turn out to be pointless for them - NOT because of any deficiency on the part of the Lord, who went the extra mile and gave them every chance, but because of their own self-hardened hearts, bent upon ignoring Him and pursuing the vanities of their own minds and their own lusts instead, with never a clean place to be found at the table of their hearts. 
Yours in Jesus Christ. 
Bob L. 
Question #3:  

Please explain the meaning of "their worm" in Isaiah 66:24.
Response #3:  

This passage is, of course, quoted by our Lord at Mark 9:48 in the context of the final state of unbelievers. It is also coupled both there and here in Isaiah 66:24 with "fire" which is said never to be "quenched". 
The unquenchable fire is a clear reference to the "lake of fire", the final place of condemnation both for human beings and angelic creatures who reject Jesus Christ (Matt.25:41; Mk.9:48; Rev.19:20; 20:10; 20:15; 21:8). It is filled by the stream of fire which proceeds for the very throne of the Father (cf. Dan.7:9-11; cf. Rev.14:10-11). 
It is in this context that we must understand "their worm", which is a further, highly descriptive reference to the torments to which the condemned will be subjected throughout all eternity. Isaiah is making his point in a poetic fashion (this chapter and most of Isaiah is in poetic form in the Hebrew text). We find a very similar usage in Isaiah 14:9-11, where the "king of Babylon" goes down "to the grave" and is covered with "maggots and worms". Isaiah is combining here a picture of the literal "grave" with that of the eternal "grave" of the non-believer. In Hebrew, the word translated "grave" is Sheol, also often translated "hell", and from the ancient Hebrew point of view, the literal earthly grave and the eternal lake of fire blend into one. This may be different from the way we might look at it today from the point of view of our modern, highly materialistic culture, but when one thinks about it from God's point of view, really, the one does precede and blend into the other. For the earthly grave is truly the "last stop" for the unbeliever's body (before the final resurrection; cf. Dan.12:2; Matt.25:46; Jn.5:29; Rev.20:11-15), while the unbeliever himself (i.e., his spirit) will be in torments from the point of physical death onward. 
Given the descriptions we have of "torments", the place of the unbelieving dead before the final resurrection (Lk.16:19-31), and those of the final "lake of fire" (Matt.25:41; Mk.9:48; Rev.19:20; 20:10; 20:15; 21:8), one is led to the conclusion that the "worm" is a symbol of earthly corruption presaging the fiery torment to come, and that, therefore, there are not literal "worms" in the final place of condemnation, but that the awful image of such things is meant to convey to those who have not yet experienced it the horror of that place. That is one reason, no doubt, why both Isaiah and our Lord use the singular, "worm", rather than the plural "worms", that is, to help us to see that this is meant to be taken as a symbol of torment and corruption instead of as a literal "worm". 
One things is certain - this is a very graphic, very vivid image. Anyone contemplating their eternal fate will not fail to "get the picture" from this earthly, earthy analogy that the prospect of coming to such an end is truly unthinkable, and (one would think and hope) respond to God as a result, seeking out His mercy and deliverance through Jesus Christ. 
Hope this is of some help. 
In Him who has delivered us from all the horrors of the grave unto a blessed and glorious eternal life, our Lord and Master Jesus Christ. 
Bob Luginbill 
http://ichthys.com