I touched on this in a thread from ages ago:
There were many traditions about patriarchs and faithful men in heaven in Second Temple Judaism, and these views influenced the NT, particularly the synoptic tradition. Enoch and Elijah were the two most common figures, as their translations were mentioned in the OT (and Elijah's return announced in Malachi), and Enoch in particular was the focus of a very large and varied cycle of literature. Elijah was believed to return by the Jews because the common belief was that he never really died and would return (cf. also the Animal Apocalypse of 1 Enoch and Revelation 11:6). The same thing was believed of Enoch. In particular, in 1 Enoch the hero was taken up to heaven and was explained the secrets of the heavenly cycles (cf. the Book of Luminaries of 1 Enoch) and thereafter Enoch became the heavenly scribe, always watching humanity and recording their deeds in the "books of life". It is precisely these books in Daniel and Revelation that will be opened on Judgment Day, for therein are recorded all the deeds by which the resurrected will be judged (cf. Revelation 20:12). In fact, in the Book of Parables (which was a direct influence on the gospels), Enoch himself was appointed to be the Son of Man (also called the Anointed One) who will come on Judgment Day seated on the throne of glory. In later Enochic tradition, Enoch was described as the great angel Metatron and even the "lesser YHWH". In Jewish tradition, other patriarchs who died had their souls taken to heaven by angels while Michael the archangel buried the body. Abraham in particular was taken up into Paradise while his body was buried in Mamre, and it is in "his bosom" where his children and grandchildren would reside (cf. Testament of Abraham). This clearly lies behind the conception in Luke 16, as well as the hope expressed in 4 Maccabees that Abraham, Isaac, and the other patriarchs will welcome the faithful martyrs when they die. Moses was another figure who was described in Jewish literature (i.e. the Assumption of Moses) as ascending to heaven at his death; the story went that Joshua saw Moses double when he died, with one Moses being taken up on a cloud to heaven while the other was buried by the angels. The anecdote in Jude 9 is dependent on the Assumption of Moses, again demonstrating the relevance of these traditions to the NT. The Exagoge of Ezekiel the Tragedian even pictures a glorified Moses in heaven being worshipped by the angels; this idea of glorification is very similar to that of Enoch in the Book of Parables and to that of Jesus in the NT. The Apocalypse of Moses reports another tradition about Adam being lifted up to third heaven to Paradise upon his death, while his body was buried in the earthly Paradise. In the Testament of Abraham, there is even a vision of Adam as the enthroned eschatological judge on Judgment Day, who exults at the souls going through the narrow gate into Paradise and who weeps sorrowfully for the souls who enter the broad and spacious gate into Gehenna. There is even a tradition about the soul of David being in heaven. In summary, the eschatology assumed in these examples is well-summarized by Josephus in the following manner: "People who depart from this life in accordance with nature's law, thus repaying what God had lent them, when the giver wants to claim it back again, win everlasting fame ... their souls remain without blemish, and obedient, and receive the most holy place in heaven. From there, when the ages come round again, they come back to live again in holy bodies" (Jewish War, 3.374; cf. Wisdom 3:1-4). See also Revelation 6:9 which pictures the faithful martyrs awaiting their future resurrection in heaven.
Regarding John 3:13, it should be noted that this passage is part of the overall proto-gnostic theology of the book (e.g. "no one has ascended into heaven" is parallel to "no one has ever seen God" in 1:18; cf. 5:37, 6:46, 14:8-9, which speaks to the Son's role as the divine Revealer of the Father) which is far removed the kind of apocalyptic Judaism described above. Remember, the Bible is not a single book but an anthology of works from different theological and eschatological standpoints.
Finally, although the above pertains to the variety of Judaisms in the Second Temple period, it should be noted that the basic premise in the Enochic corpus that Enoch was taken up to heaven is most likely presumed in the much less detailed bare-bones reference in Genesis 5:24. It is often noted that this brief notice alludes to a backstory that would have already been widely known outside of Genesis (just as the bare references to Cain, Balaam, and Korah in Jude 11 allude to the backstories of these figures in the OT), and the diversified corpus of Enochic tradition (including the Book of Luminaries, the Book of Giants, the Book of Parables, the Book of Giants, the Animal Apocalypse, the Apocalypse of Weeks, the Epistle of Enoch, Jubilees, etc.) is a witness to the body of tradition that existed earlier, especially since it is filled with elements derived from much older Babylonian and Canaanite mythology. In fact, there is considerable evidence that the figure of Enoch himself is based on Babylonian myths about the antedilivian king Enmeduranki (who was seventh in line from the first man), who was similarly associated with the sun (= the solar calendar of Enoch and the 365 years of Enoch in Genesis) and who was initiated into the secrets of heaven. This was discussed in another very old thread of mine: http://www.jehovahs-witness.com/10/67655/1.ashx