Now to the other commentaries. We will begin with the general and go to the specific.
 
From the Matthew Henry Main for verse 20:
 
Another thing that may comfort us is that though there are some whose faith is overthrown, yet there are others who keep their integrity, and hold it fast (2 Timothy 2:20): In a great house there are not only vessels of gold, etc. The church of Christ is a great house, a well-furnished house: now some of the furniture of this house is of great value, as the plate in a house; some of small value, and put to mean uses, as the vessels of wood and earth; so it is in the church of God. There are some professors of religion that are like the vessels of wood and earth, they are vessels of dishonour. But at the same time all are not vessels of dishonour; there are vessels of gold and silver, vessels of honour, that are sanctified and meet for the Master's use. When we are discouraged by the badness of some, we must encourage ourselves by the consideration of the goodness of others. Now we should see to it that we be vessels of honour: we must purge ourselves from these corrupt opinions, that we may be sanctified for our Master's use. Observe,
 
1. In the church there are some vessels of honour and some of dishonour; there are some vessels of mercy and other vessels of wrath, Romans 9:22-23. Some dishonour the church by their corrupt opinions and wicked lives; and others honour and credit it by their exemplary conversation.
 
Quoted verse:
Romans 9:22-23
22 What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
23 And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
 
 Let us look at part of the commentary on Romans 9:22 so we can understand the reference to it.

Now back to the points for our verse tonight from the Matthew Henry Main:
 
2. A man must purge himself from these [corrupt opinions, false doctrines and wicked lives] before he can be a vessel of honour, or meet for his Master's use.
 
3. Every vessel must be fit for its Master's use; every one in the church whom God approves must be devoted to his Master's service and meet for his use.
 
4. Sanctification in the heart is our preparation for every good work. The tree must be made good, and then the fruit will be good. ~Matthew Henry Main
 
Now to the Matthew Henry Concise which covers verses 14-24
 
Those disposed to strive, commonly strive about matters of small moment. But strifes of words destroy the things of God. The apostle mentions some who erred. They did not deny the resurrection, but they corrupted that true doctrine. Yet nothing can be so foolish or erroneous, but it will overturn the temporary faith of some professors. This foundation has two writings on it. One speaks our comfort. None can overthrow the faith of any whom God hath chosen. The other speaks our duty. Those who would have the comfort of the privilege, must make conscience of the duty Christ gave himself for us, that he might redeem us from all iniquity, Titus 2:14. The church of Christ is like a dwelling: some furniture is of great value; some of smaller value, and put to meaner uses. Some professors of religion are like vessels of wood and earth. When the vessels of dishonour are cast out to be destroyed, the others will be filled with all the fullness of God. We must see to it that we are holy vessels. Everyone in the church whom God approves, will be devoted to his Master's service, and thus fitted for his use. ~Matthew Henry Concise
 
Here is something from the Biblical Illustrator

Holiness and service
Through the whole of Scripture we find that whatever God sanctifies is to be used in the service of His holiness. Holiness and selfishness, holiness and inactivity, holiness and sloth, holiness and helplessness, are utterly irreconcilable. Whatever we read of as holy was taken into the service of the holiness of God. Holiness is essential to effectual service. In the Old Testament we see degrees of holiness, not only in the holy places, but as much in the holy persons. In the nation, the Levites, the priests and then the High Priest, advance from step to step; as in each succeeding stage the circle narrows, and the service is more direct and entire, so the holiness required is higher and more distinct. It is even so in this more spiritual dispensation; the more of holiness, the greater the fitness for service; the more there is of true holiness the more there is of God, and the more true and deep is the entrance He has had into the soul. The hold He has on the soul to use it in His service is more complete. ~Biblical Illustrator

Quoted verse:
Titus 2:14
Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.

Now to the specific commentaries. Let us read verse 21 again:

2 Timothy 2:21
If a man therefore purge himself from these, he shall be a vessel unto honour, sanctified, and meet for the master's use, and prepared unto every good work.

Only one commentary I found broke the verse out in parts and that was the John Gill.

1] If a man therefore purge himself from these.
2] He shall be a vessel unto honour.
3] Sanctified.
4] And meet for the master's use
5] And prepared unto every good work

1] If a man therefore purge himself from these.
If a man therefore purge himself from these - That is, as Bengel puts it, ‘if any one shall by purifying himself have gone out of their number.’ The compound verb ‘purge out’ only occurs besides in 1 Corinthians 5:7 where the preposition gives the force ‘purge out from your houses the old leaven.’ Wordsworth forcibly notes here; ‘a man may at one time of his life be numbered among vessels to dishonour, and yet may become a vessel to honour, by cleansing himself out from their number and condition. Mark this assertion of Free Will.’ And again, ‘a Christian man may not go out of the great house which is the Visible Church of God: he cannot separate himself wholly from sinners, but he must cleanse himself from them as sinners; that is, he must not communicate with them in their sins.’ ~Cambridge

Quoted verse:
1 Corinthians 5:7
Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us:

If a man therefore purge himself from these - He that takes heed to his ways and to his doctrines, and walks with God, will separate himself, not only from all false doctrine, but from all wicked men, and thus be sanctified and proper to be employed by the Master in every good word and work. The apostle has not made the application of these different similes, and it is very difficult to tell what he means. ~Adam Clarke

If a man therefore purge himself from these - That is, if a man clears himself, and keeps himself clear from such men as Hymenaeus and Philetus, who are comparable to wooden and earthen vessels, and are dishonourable ones; if he shuns their defiling company, and polluting principles; if he keeps clear of their heresies, and is not carried away with the errors of these wicked men, and is not drawn aside by them into immoral practices, but stands fast in the faith, and departs from iniquity: ~John Gill

If a man therefore purge himself from these - If a man wishes to be a noble vessel, of gold, for honorable uses in the Lord's house, let him cleanse himself from earthly lusts. ~People's New Testament

If a man purge himself from these - Vessels of dishonour, so as to have no fellowship with them. ~John Wesley Explanatory Notes

The next commentary is from the Pulpit Commentary.

THE DUTY OF SEPARATION FROM THE VESSELS OF DISHONOUR. "If a man therefore purge himself from these, he shall he a vessel unto honour, sanctified, meet for the Master’s use, prepared unto every good work." The thought of separation from the false teachers was, no doubt, uppermost in the apostle’s mind, but it has a wider scope.

1. It is our duty to withdraw from error. This withdrawal may be effected in several ways. The apostle says to Timothy, "From such withdraw thyself" (1 Timothy 6:5); he says to Titus, "A man that is a heretic avoid" (Titus 3:10). The separation may take place by the heretic being cast out of communion; or avoided in the intercourse of life; or, in the last resort, the believer may withdraw himself from the society which fails to cast him out. Or the believer may be called upon to "purge himself"—terms which seem to imply personal defilement in a separate walk of holiness and purity. He must purge himself from heresy and impurity.

2. The right dedication and destination of the vessel for honour.
(1) He will become "sanctified," in its double sense consecrated to God and walking in the purity of a separated life.
(2) He will be serviceable to the Master of the house in all the various ministries to which he may be called.
(3) He will be prepared unto every good work. Unlike the unwise and the evil man, who is to all good works reprobate, he is, as created in Christ Jesus unto good works, enabled to run in the way of the Lord’s commandments. ~The Pulpit Commentary

Quoted verses:
1 Timothy 6:5 [see Lesson]
Perverse disputings of men of corrupt minds, and destitute of the truth, supposing that gain is godliness: from such withdraw thyself.

Titus 3:10
A man that is an heretick after the first and second admonition reject;

2] He shall be a vessel unto honour.
If a man therefore purge himself from these, he shall be a vessel unto honour - If a man “cleanse” or “purify” himself; compare John 15:2. The word “these” refers, here, to the persons represented by the vessels of wood and of earth - the vessels made to dishonor, as mentioned in the previous verse 2 Timothy 2:20. The idea is, that if one would preserve himself from the corrupting influence of such men, he would be fitted to be a vessel of honor, or to be employed in the most useful and honorable service in the cause of his Master. On the word “vessel,” see Acts 9:15. ~Barnes Notes

Quoted verses:
John 15:2
Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit.

2 Timothy 2:20 [see Lesson]
But in a great house there are not only vessels of gold and of silver, but also of wood and of earth; and some to honour, and some to dishonour.

Acts 9:15 ...Jesus speaking of Paul
But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:

He shall be a vessel unto honour - he will be made manifest, and appear to be a vessel chosen to honour; and will be an honourable member of the church here, and will be honoured by Christ hereafter: ~John Gill

3] Sanctified.
Sanctified - he will appear to be one that is set apart by God the Father, and whose sins are purged away by the blood of Christ, and who is sanctified internally by the Spirit of God; for external holiness springs from internal holiness, and is, an evidence of it: ~John Gill

4] And meet for the master's use.
And meet for the master’s use - Suitable to be employed by the Lord Jesus in promoting his work on earth. ~Barnes Notes

And meet for the master's use - the use and service of Christ, who is the master of the house; either for the ministry of the word, the administration of ordinances, or for some service or another, which he calls him to, and employs him in. ~John Gill

5] And prepared unto every good work.
And prepared unto every good work - which an unregenerate man is not; he is to every good work reprobate; he is not capable of performing good works; he is not prepared for them, nor ready at them; but a true believer, one that is regenerated, and sanctified by the Spirit of God, he is created in Christ Jesus unto good works; and has in the performing of them right principles, aims, and ends, as well as a supply of grace, by which he is enabled to do them. ~John Gill