What is the Biblical basis for the belief that there are humans in heaven now? Most Christians believe that Enoch, Elijah, Moses, the thief on the cross who was pardoned by Jesus and all the saints who were resurrected during the crucifixion were all translated to heaven.

What is the Biblical evidence for this belief?
There are no explicit statements in the Bible that any of the people mentioned in the question are now in heaven. The belief on the part of many Christians that they are now in heaven is based on reading key Bible passages about their death and their status after death in light of a more generalized belief that humans go to heaven after they die.
On the people specifically mentioned in the question, here are the Bible passages commonly quoted to support a belief that they are now in heaven:
Enoch

Thus all the days of Enoch were three hundred sixty-five years. Enoch walked with God; then he was no more, because God took him. (Genesis 5:23-24)

And:

By faith Enoch was taken so that he did not experience death; and &quot;he was not found, because God had taken him.&quot; For it was attested before he was taken away that
&quot;he had pleased God.&quot; (Hebrews 11:5)

Neither of these passages state that Enoch is in heaven now. But in light of the generalized belief among many Christians that people go to heaven after they die, these verses are read by such Christians as meaning that God took Enoch directly to heaven.
Moses &amp; Elijah
These two are taken together because the Bible passages most commonly referred to as saying that they are now in heaven are the accounts of the Transfiguration of Jesus in the Synoptic Gospels. The full accounts are found in Matthew 17:1-13; Mark 9:2-8; Luke 9:28-36.
Here are the verses from these accounts in which Moses and Elijah are specifically mentioned, with the lead-in verse about the transfiguration of Jesus quoted only for the first one:

And [Jesus] was transfigured before them, and his face shone like the sun, and his clothes became dazzling white. Suddenly there appeared to them Moses and Elijah, talking with him. Then Peter said to Jesus, &quot;Lord, it is good for us to be here; if you wish, I will make three dwellings here, one for you, one for Moses, and one for Elijah.&quot; (Matthew 17:2-4)
And there appeared to them Elijah with Moses, who were talking with Jesus. Then Peter said to Jesus, &quot;Rabbi, it is good for us to be here; let us make three dwellings, one for you, one for Moses, and one for Elijah.&quot; (Mark 9:4-5)
Suddenly they saw two men, Moses and Elijah, talking to him. They appeared in glory and were speaking of his departure, which he was about to accomplish at Jerusalem. Now Peter and his companions were weighed down with sleep; but since they had stayed awake, they saw his glory and the two men who stood with him. Just as they were leaving him, Peter said to Jesus, &quot;Master, it is good for us to be here; let us make three dwellings, one for you, one for Moses, and one for Elijah&quot;—not knowing what he said. (Luke 9:30-33)

Here Moses and Elijah appear with Jesus, very much alive, and in the Luke account even &quot;appearing in glory&quot; and talking about upcoming events. The three disciples who witnessed this event perceived Moses and Elijah as being present in person with them—hence Peter's offer to make dwellings for all three figures: Jesus, Moses, and Elijah.
The natural conclusion for Christians who believe that human beings go to heaven right after death is that Moses and Elijah could appear with Jesus because they are not still in the grave awaiting resurrection, but are currently very much alive and well and living in heaven.
The thief on the cross
Of all the figures mentioned in the question, the incident of the thief on the cross comes closest to providing an explicit statement that a human being is now in heaven. Here is the full passage:

One of the criminals who were hanged there kept deriding him and saying, &quot;Are you not the Messiah? Save yourself and us!&quot; But the other rebuked him, saying, &quot;Do you not fear God, since you are under the same sentence of condemnation? And we indeed have been condemned justly, for we are getting what we deserve for our deeds, but this man has done nothing wrong.&quot; Then he said, &quot;Jesus, remember me when you come into your kingdom.&quot; He replied, &quot;Truly I tell you, today you will be with me in Paradise.&quot; (Luke 23:39-43)

Here Jesus tells the repentant thief, who witnessed to his fellow thief on the cross, &quot;Truly I tell you, today you will be with me in Paradise&quot; (Luke 24:43).
Some have argued that since there is no punctuation in the original Greek, it could read instead, &quot;Truly I tell you today, you will be with me in Paradise,&quot; so that it could refer to a future resurrection to Paradise. However, that would be a somewhat strained parsing of the Greek. That's why it is almost always translated in the traditional manner, as &quot;today you will be with me in Paradise.&quot; In the list of all translations of Luke 24:43 at BibleGateway, though the specific wording varies, every single translation interprets the verse this way.
Though &quot;Paradise&quot; is not necessarily identical to &quot;heaven,&quot; most Christians do interpret &quot;Paradise,&quot; especially when it is mentioned in the New Testament, as a reference to heaven.
The saints who were resurrected during the crucifixion
Here is the relevant passage in its context:

Then Jesus cried again with a loud voice and breathed his last. At that moment the curtain of the temple was torn in two, from top to bottom. The earth shook, and the rocks were split. The tombs also were opened, and many bodies of the saints who had fallen asleep were raised. After his resurrection they came out of the tombs and entered the holy city and appeared to many. Now when the centurion and those with him, who were keeping watch over Jesus, saw the earthquake and what took place, they were terrified and said, &quot;Truly this man was God’s Son!&quot; (Matthew 27:50-54)

Here there is no explicit statement that these saints who were raised from the dead (or from having &quot;fallen asleep,&quot; to use the Biblical term) went to heaven. It says only that they were raised, came out of the tombs, and entered the holy city—meaning Jerusalem—and appeared to many people there. However, the idea that they would then go back into their tombs after being resurrected seems unlikely to many Christians. So many Christians believe that they then went on to heaven.
Other Bible passages providing support for humans now being in heaven
As I mentioned earlier, none of these Bible passages about the figures specifically mentioned in the question explicitly and unequivocally say that these people are now in heaven. In fact, no matter what passages you care to quote, there are Christians who dispute that they point to humans currently being in heaven.
Having said that, here are a few other passages in the Bible that can easily be read as saying that there are humans currently residing in heaven.
First, two passages from the Gospels:

&quot;And as for the resurrection of the dead, have you not read what was said to you by God, 'I am the God of Abraham, the God of Isaac, and the God of Jacob'? He is God not of the dead, but of the living.&quot; And when the crowd heard it, they were astounded at his teaching. (Matthew 22:31-33, and see the parallel passages in Mark 12:26-27; Luke 20:37-38)

Here Jesus uses the example of the words of God at the burning bush (in Exodus 3:6) in support of a resurrection. And the way he interprets God's words make it clear that he is speaking of Abraham, Isaac, and Jacob as being alive now, not still dead in their graves awaiting a future resurrection.
Another passage from the Gospels that speaks of human beings currently alive in the afterlife is Jesus' story of the rich man and Lazarus in Luke 16:19-31. Here is the most relevant part of the story:

The poor man died and was carried away by the angels to be with Abraham. The rich man also died and was buried. In Hades, where he was being tormented, he looked up and saw Abraham far away with Lazarus by his side. (Luke 16:22-23)

Here Jesus speaks of two men dying and immediately being carried to their place either with Abraham (commonly interpreted as heaven) or in Hades, the Greek word for the underworld. The entire action and dialogue of the story is presented as currently taking place in the afterlife. And even if this is read as a parable rather than as Jesus narrating a literal occurrence, his reference to these two people being immediately carried to their eternal dwelling place supports the idea of immediate resurrection of human beings to heaven (or hell) after death.
And two passages from the book of Revelation:

After this I looked, and there was a great multitude that no one could count, from every nation, from all tribes and peoples and languages, standing before the throne and before the Lamb, robed in white, with palm branches in their hands. They cried out in a loud voice, saying, &quot;Salvation belongs to our God who is seated on the throne, and to the Lamb!&quot; (Revelation 7:9-10)

Here John describes seeing a huge crowd of people from every nation standing before God's throne and praising God. And though the book of Revelation is commonly interpreted as referring to future events, John narrates it in the present tense, as things he was currently seeing in heaven. This is therefore another passage providing Biblical support for Christians to believe that humans go to heaven directly after death.

When he opened the fifth seal, I saw under the altar the souls of those who had been slaughtered for the word of God and for the testimony they had given; they cried out with a loud voice, &quot;Sovereign Lord, holy and true, how long will it be before you judge and avenge our blood on the inhabitants of the earth?&quot; They were each given a white robe and told to rest a little longer, until the number would be complete both of their fellow servants and of their brothers and sisters, who were soon to be killed as they themselves had been killed. (Revelation 6:9-11)

Here the book of Revelation speaks of souls slaughtered as pleading their case, receiving white robes, and being told to &quot;rest,&quot; or wait, a while longer. This implies that they are currently alive in some state, which is most easily interpreted as their being alive in some part of heaven.
This is by no means an exhaustive list of passages providing Biblical support for the belief that there are humans in heaven now. But these are a few of the key passages related to the question.
Even more broadly, it has become a common belief among Christians that human beings become angels, and that this happens immediately after death. For the Biblical basis of this belief, see this Christianity.SE question: What is the biblical basis for humans becoming angels after they die?
On the origins of this belief in Christian history, see this Christianity.SE question: What is the source of the belief that the deceased become angels?