What is the Biblical argument used by Evangelical Christians against the Catholic doctrine of the invocation of the saints?

The question correctly emphasizes that intercession of the saints and invocation of the saints are not the same doctrines. Both are taught in Catholicism but only the former is taught in Evangelical Christianity.

The New Testament is explicit that the saints in heaven intercedes for the saints on earth:

"And the smoke of the incense of the prayers of the saints ascended up before God from the hand of the angel".

Revelations 8:4

In fact, the Old Testament concurs:

If there shall be an angel speaking for him . . . He shall have mercy on him, and shall say: Deliver him, that he may not go down to corruption" Job 33:23-24

And the non-inspired Jewish literature also agrees:

When thou didst pray with tears… I (Archangel Raphael) offered thy prayer to the Lord.

Tobit 7:12

The Bible (both OT & NT) and the Apocrypha both show that saints in heaven pray for people on earth without these people on earth asking for it.

However, there is not one scripture which says that we should invoke/pray/ask the saints in heaven to pray for us saints on earth.

Evangelical Christians believe in the intercession of the saints ( both in heaven and on earth) but not the invocation of the saints. We do not need to invoke/ pray/ ask the saints in heaven to pray for us who are on earth(source).

We have no scriptural record of the invocation of the saints in heaven in both the OT and the NT.

Rather, the only scriptural record which positively approves invoking someone in heaven for his intercession is the invocation and intercession of God the Son (John 14:14; Romans 8:34).

Jesus Christ himself said that we may ask Him anything in his name and in fact, he's the one who'll do it:

You may ask me for anything in my name, and I will do it.

John 14:14

No OT saint or NT saint ever spoke of invocation of the saints.

In the entire Scriptures (both OT & NT) only God is the recipient of prayers.

Philippians 4:6 highly implies that we should only pray to God:

Do not be anxious about anything, but in everything by prayer and supplication** with thanksgiving let your requests be made known to God.

Philippians 2:6

What is the Biblical argument used by Evangelical Christians against the Catholic doctrine of the invocation of the saints?

We can see a principle of equality with other Christians (and even angels) in our work for the Lord that would preclude elevated status for some.

Revelation 19:10 And I fell at his feet to worship him. And he said unto me, See thou do it not: I am thy fellowservant, and of thy brethren that have the testimony of Jesus: worship God: for the testimony of Jesus is the spirit of prophecy.

Each Christian has direct access to the Father and needs no intermediary.

John 14:23 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.

John 16:26-27 At that day ye shall ask in my name: and I say not unto you, that I will pray the Father for you: For the Father himself loveth you, because ye have loved me, and have believed that I came out from God.

We have the Spirit of God living within us. We have no need of some dead person to talk to God for us?

John 15:26 But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:

While the Bible does use the word “saint”, it is used of all believers and not of just special believers. It is meant to distinguish those who have been set aside from the world and not set aside from other believers. All “saints” are expected to grow into Christ-likeness.

Ephesians 4:11-12 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers; For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ:

The most convincing verse is;

1 Timothy 2:5 For there is one God, and one mediator between God and men, the man Christ Jesus;

Prayer can be hindered by sin, bad conduct, and wrong motives.

Psalm 66:18 If I regard iniquity in my heart, the Lord will not hear me:

1 Peter 3:7 Likewise, ye husbands, dwell with them according to knowledge, giving honour unto the wife, as unto the weaker vessel, and as being heirs together of the grace of life; that your prayers be not hindered

James 4:3 Ye ask, and receive not, because ye ask amiss, that ye may consume it upon your lusts.

However, there is no record of prayers made to saints. All prayer is assumed to be to God.

1 Peter 3:12 For the eyes of the Lord are over the righteous, and his ears are open unto their prayers: but the face of the Lord is against them that do evil.

We can solicit prayers from other believers and we know that prayers from those who are closer to God are effective.

James 5:16 Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much.

However, there is no record of anything done by those who are dead other than wait for the resurrection.

Our communication with God is described as one of a child with his father not of a child through a servant to his father.

Galatians 4:6 And because ye are sons, God hath sent forth the Spirit of his Son into your hearts, crying, Abba, Father.

There are two main Protestant arguments against asking the deceased saints to intercede for us:

1. It is seen as contradicting the Bible's prohibition on contacting the dead. These are found most clearly in the Jewish Law, which is not binding on Christians, but is still considered to be solid wisdom in this case.

   Do not turn to mediums or seek out spiritists, for you will be defiled by them. I am the Lord your God. (Leviticus 19:31, NIV)

   Let no one be found among you who sacrifices their son or daughter in the fire, who practices divination or sorcery, interprets omens, engages in witchcraft, or casts spells, or who is a medium or spiritist or who consults the dead. (Deuteronomy 8:10-11)

2. It is thought that asking the saints to intercede for us is at best a waste of time, and at worst idolatrous, because Jesus is the best and perfect mediator, and no human can remotely compare to him. And while not all who do believe in the intercession of the saints think this way, there are many people who think that we are too sinful, too unworthy to directly approach Jesus in prayer, and for our requests to be heard we must go through Mary or the saints. Evangelical Protestants would consider this to be a gross distortion of the gospel.

   For there is one God and one mediator between God and mankind, the man Christ Jesus (2 Timothy 4:5)

   Now there have been many of those priests, since death prevented them from continuing in office; but because Jesus lives forever, he has a permanent priesthood. Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them. (Hebrews 7:23-25)

   This argument may not be very strong, because Protestants don't hesitate to ask living Christians to pray for them, but it's still an argument that gets made.

3. A third, more minor, argument is an argument from silence: this practice is not recognised as being taught or performed anywhere in the Bible.

This position ultimately arises from a different understanding of the Communion of Saints in Protestantism. Protestants would not deny the real union of living believers (the church militant) nor the union of believers who have passed away (the church triumphant), but they would generally not say that there is a functional union between those groups. We are united in our shared salvation state, our faith, our creed, our shared indwelling of the Spirit, our hope, and our inheritance, but we are not united with the dead in any relational capacity. There is much disagreement within Protestantism over the nature of the Intermediate State between death and resurrection, and many believe in soul sleep, that the dead are unconscious until the time of their resurrection. Others may believe that they are conscious, but that they do not have the means to hear our invocations and prayers.