These verses use what is known as phenomenological language, the language of appearances. Phenomenological language occurs when we describe something as it looks, irrespective of how it is. The classic example of phenomenological language is talk of the sun rising and setting. The sun appears to rise and set , but this motion is actually due to the rotation of the earth rather than to motion of the sun around the earth.
Verses that speak of the dead sleeping use phenomenological language. For example, Daniel 12:2 states, "And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt." This image is of people getting up much as a sleeper rises in the morning. The sleep being discussed is phenomenological sleep, not literal sleep (Daniel is not talking about living people who sleep on the ground). Because dead people look like they are sleeping, especially when lying on their deathbeds (and notice that people often die on beds, enhancing the sleep analogy), the Bible often uses "sleep" as a euphemism for "death." In fact, this euphemism is common today.
There are two versions of the "soul sleep" theory.
The Jehovah's Witness claims that the soul ceases to exist at death and then is re-created by God at the resurrection. If their theory were true and there were no soul which survives death, it is difficult to see why the re-created "you" is not just a copy of you. It may have all your memories, but it is hard to see why it is not just a copy. If God had created this copy while you still existed, the fact it is a copy rather than the real you would be obvious.
If it is a copy, that causes problems of justice. Because you ceased to exist, you--the real you--were never punished for your sins or rewarded for your good deeds; you simply ceased to exist. Similarly, the copy of you which was created on the Last Day is then punished or rewarded for things it never did.
Once one has distinguished between the Jehovah's Witnesses' view and the view that claims that our souls simply sleep between death and resurrection, one can go on to refute these ideas by using the Bible. The following verses apply to both versions of the doctrine.
In Revelation 6:9-10, John writes, "When he [Christ] opened the fifth seal, I saw under the altar the souls of those who had been slain for the word of God and for the witness they had borne; they cried out with a loud voice, 'O Sovereign Lord, holy and true, how long before thou wilt judge and avenge our blood on those who dwell upon the earth?'"
Here John sees the disembodied souls of early Christian martyrs. The fact they are disembodied is known because they have been slain. Thus disembodied souls exist. The fact they are conscious is known because they cry out to God for vengeance. Unconscious people can't do that. Thus conscious, disembodied souls exist.
In Revelation 20:4 John sees these souls again: "Then I saw . . . the souls of those who had been beheaded for their testimony to Jesus and for the word of God and who had not worshipped the beast or its image and had not received its mark on their foreheads or their hands. They came to life and reigned with Christ a thousand years."
Here again we have disembodied souls (they had been beheaded). John sees them coming to life to reign with Christ--hence they are in a pre-resurrection state. Some scholars argue that this is a spiritual resurrection rather than a physical one. Even if that were so, it would only strengthen the case for conscious, disembodied souls because, after having been beheaded, they would be reigning with Christ in heaven in a disembodied state.