How do LDS reconcile Ephesians 3:17 and D&C 130:3?

So how do the Lds reconcile this glaring contradiction?

Easily, because there is no contradiction. You left out the theological context given in the remainder of this section, which is impossible to misunderstand once you have read it:

"The Father has a body of flesh and bones as tangible as man's; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit. Were it not so, the Holy Ghost could not dwell in us." (Doctrine and Covenants 130:22)

The Conscience is called the Light of Christ. @depperm is right in that it is not possible for Christ to dwell in us in the same sense as the Holy Ghost; the Son (Christ) clearly asks the Father "That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us" (John 17:21). "As thou, Father, art in me" clearly refers to a presence or dwelling that is not of the physical body, since both The Father and the Son have physical bodies, and moreover it is made expressly clear that it is their unity of purpose that is being emphasized, not any alleged sameness of physical presence. Jesus said at various times "my Father is with me" even while physically absent from His Father. This is apparently the oneness spoken of, not any kind of transsubstantiation or "transpersonation", if any such concept is thought to exist. On the cross, He said, "My God, My God, why hast Thou forsaken me?" indicating a withdrawal of the Father's light and sustaining influence.

After His resurrection, He said, "Handle me and see, a spirit hath not flesh and bones as ye see me have." Mainstream Christians embraced this reality just around a century ago. It seems this faith has since dwindled.

Yet these Scriptures put the final nails in the coffin of any theories of non-physicality, or of non-distinctness of the Persons of the Father and the Son.

"Have ye received the Holy Ghost since ye believed?"

(The Holy Ghost is rightly called the Lord's Holy Spirit, because He is one with the Lord and does His bidding.)

In summary, the answer is simple: The Holy Ghost can dwell in us, as attested by Scripture from that same section. The Light of Christ (knowledge of good and evil) was given to us from birth, and Christ being "in us" is metaphorical, not physical, consistent with the testimony of the Savior given during His Great Intercessory Prayer. Additional Scripture highlights that we will have "His image in our countenances" if we have obeyed Him and are like Him. Is that image His physical presence? No, but how often have we heard someone say they could see your father or mother in you, meaning in your countenance, or that you are one with someone else? God speaks to our understanding and these are clearly not expressions of cophysicality or possession by a spirit, but rather of shared heritage and unity.

Moreover the name of Christ can be written on our hearts, and love for Him can dwell in our hearts. We find this easy to conceptualize in human relationships but for some reason it is taken to be theologically taxing. Nonetheless God intends for us to learn this lesson. He can be "in our hearts" without physically residing there, if we will simply turn our hearts over to Him and place all of the desires of our hearts in Him.

The same way we understand John 14:10:

Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works.

That something more transcendent than physical oneness is intended can be seen by flipping ahead a few chapters to the great intercessory prayer. In John 17:

6 I have manifested thy name unto the men which thou gavest me out of the world: thine they were, and thou gavest them me; and they have kept thy word.

11 And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.

22 And the glory which thou gavest me I have given them; that they may be one, even as we are one:

23 I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.

26 And I have declared unto them thy name, and will declare it: that the love wherewith thou hast loved me may be in them, and I in them.

Notice also the similar language in John 14:20

At that day ye shall know that I am in my Father, and ye in me, and I in you.

Jesus speaks of His disciples being one with Him in the same way He is one with the Father. That the disciples are distinct beings from Jesus is not in doubt. In what sense then are they one? And in what sense will the Father and the Son make their abode with the disciples?

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The Love of God

Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him. (John 14:23)

In both chapters 14 & 17, the discussion of oneness is immediately accompanied by a discussion of love. When God’s love is in us—genuinely—we do God’s works. Jesus had the Father’s love in Him perfectly, and He did Father’s work perfectly (see John 14:10).

Love brings unity in a transcendent way—and Jesus wants that love to dwell in His disciples to make more of them—and their labors—things that could never be achieved on their own (see this applied in the parable of the vine in John 15:1-12). He does not wish for them to obey out of fear, transactional incentive, or even duty—He wants them to obey out of love.

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He’s going…but not leaving?

But there’s more. In both chapters 14 & 17 the discussion of oneness is accompanied by a discussion of going to the Father. That the Father is not physically present is evident by Jesus’ repeated statement that He’s going somewhere else.

Much of the context of chapter 14 is seen in verses 2 & 3:

2 In my Father’s house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.

3 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.

Jesus has indicated that there is glory for His disciples—apparently some now and some hereafter. Jesus is telling them that He is preparing a place for them in heaven—but that they can experience Divine presence before then—the promise He gives in this chapter, right after the discussion of love, indicates how this can happen:

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The Holy Ghost

26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.

27 Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid. (John 14:26-27)

The discussion has now gone full circle from verse 1—Jesus told them not to be troubled and explained to them the Comforter He would give them. He’s leaving them in the world, but He is not leaving them without His or His Father’s companionship, through the Holy Ghost.

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Conclusion

Jesus in John & Paul in Ephesians speak not of physical things, but of spiritual things. Despite having plainly told them He is going away (He’s about to die, and will before long ascend to heaven), He has promised that He will come to them, and He will soon pray that they may be one with Him. This coming will not be constant physical companionship, but the inestimable gift of the Holy Ghost:

17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.

18 I will not leave you comfortless: I will come to you. (John 14:17-18)

The Holy Ghost is a perfect representative of Jesus & the Father; Jesus is a perfect representative of the Father (see verse 9). The unity of the members of the Godhead is given in chapter 17 as an example—Jesus wants His disciples to become more perfect representatives of Him. One won’t lead you anywhere different from where another would. In the case of the Godhead, you cannot please one without pleasing all; you cannot truly worship one without worshipping all. Jesus promises the disciples that if they love Him and keep His words, they can enjoy the constant presence of a member of the Godhead.

In this way, Jesus has always had His Father with Him. In this way, Jesus will come to them, make His abode with them, dwell in their hearts, and be one with them, even while not physically present.

Note that all of the above was presented using only the Bible. If you'd like Book of Mormon references teaching these ideas, Alma 34:34-36 is a worthwhile place to start.

The LDS believe the godhead to be 3 distinct beings, as opposed to the trinity.¹ So there is no contradiction.

In Regards to John 14:16,23

16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;

Jesus is talking about the Holy Spirit abiding with them forever because he will die and no longer be with them.² The Holy Ghost doesn't have a body and can stay with them when Jesus is gone.

23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.

As D&C 130:3 explains this is a is a personal appearance not a spiritual (I am not saying this wouldn't be a spiritual experience) dwelling/visitation because the LDS believe in 3 distinct individuals.

Colossians 1:27

27 To whom God would make known what is the riches of the glory of this mystery among the Gentiles; which is Christ in you, the hope of glory:

I will refer to the commented John 17:22-23

22 And the glory which thou gavest me I have given them; that they may be one, even as we are one:

23 I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.

These verses are talking about being one in purpose or glory like the godhead (Jesus Christ, Heavenly Father, and the Holy Spirit).

Ephesians 3:17 doesn't change LDS belief. This is talking about purpose. Since the LDS believe in distinct personages, and Jesus Christ has a body he cannot physically dwell in your heart.

Romans 10:10

10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.

As Christ set the example of righteousness; by accepting and following him, it can be said Christ/righteousness dwells in you.

_{1 Biblical basis of distinct persons}

_{2 New Testament Study Guide}