What is the biblical basis for interpreting "born again", "baptized in the Holy Spirit" and "filled with the Holy Spirit" as different experiences?

If you want a full list of every denomination's doctrinal and traditional interpretations of these terms, you're not going to get it.

But if all you want is a simple biblical explanation of the terms, then consider these example usages. (Note that each succeeding one is accepted by fewer denominations.)

Human spirit:

Thus says the LORD, who stretches out the heavens, lays the foundation of the earth, and forms the spirit of man within him: — Zechariah 12:1

But there is a spirit in man, And the breath of the Almighty gives him understanding. — Job 32:8

Humans are born already possessing a spiritual nature. It is this spirit that makes us self-aware and distinguishes us from animals.

Filled with the holy spirit:

“And I have filled him with the Spirit of God, in wisdom, in understanding, in knowledge, and in all manner of workmanship, — Exo 31:3

When they came there to the hill, there was a group of prophets to meet him; then the Spirit of God came upon him, and he prophesied among them. — 1Samuel 10:10

And when they had prayed, the place where they were assembled together was shaken; and they were all filled with the Holy Spirit, and they spoke the word of God with boldness. — Acts 4:31

Sometimes people receive a boost, filling them with extra spirit. (This would typically be to accomplish some task for God, or as a result of requesting help for some specific purpose.)

But the Spirit of the LORD departed from Saul, and a distressing spirit from the LORD troubled him. — 1Samuel 16:14

This guiding spirit may last a lifetime or be only temporary, and may come upon anyone, regardless of whether they have been baptized into Christ.

Baptized in the holy spirit:

Then Peter said to them, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. — Acts 2:38

To become a Christian, one must repent (change one's behaviour and attitude) and then be baptized. During this ceremony, one will receive a special portion of God's holy spirit, as a gift, not as something that can be earned or deserved.

Born again:

“That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. Do not marvel that I said to you, ‘You must be born again.’ The wind blows where it wishes, and you hear the sound of it, but cannot tell where it comes from and where it goes. So is everyone who is born of the Spirit.” — John 3:6–8

Being "born again" in this case does not refer to the "I feel like a new man!" emotion that many people experience when they discover a new way of looking at things.

Jesus literally meant what he said; born again Christians will no longer be physical beings. They will be able to move anywhere, freely, not being constrained by physical obstacles.

And He is the head of the body, the church, who is the beginning, the firstborn from the dead, that in all things He may have the preeminence. — Colossians 1:18

For whom He foreknew, He also predestined to be conformed to the image of His Son, that He might be the firstborn among many brethren. — Romans 8:29

Following his Resurrection, Jesus became the firstborn from the dead of many spiritual beings, the literal sons of God.

Interpretation:

Our human spirits (what we think of as "ourselves") were combined at baptism with God's holy spirit, in a manner similar to physical conception. That combined spirit not only guides us, it also grows and develops within us like a human fetus, destined to eventually be born as a child of God.

in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal must put on immortality. — 1Corinthians 15:52–53

When Christ returns, Christians, both dead and still alive, will lose their physical bodies and their embryonic spirits will be reborn as one of Jesus's siblings, no longer in the physical image of God, but now in the spiritual image of God.