I can only quote from the article of prof Davies, Ben, but I fear that there is so much in the article that I cannot copy all (and especially the more strong arguments).
Perhaps - and I should point out this ''perhaps'' to be not so reductive - the more strong argument of Davies is the following:
ARGUMENT FROM THE IMPROBABILITY OF A DEPENDENCE 1 FROM N AS OPPOSED TO A DEPENDENCE N FROM 1.
Lattke writes that ''the dependence of the Odes of Solomon on - or their relation to - the Johannine corpus (especially Jon and 1 John) has always been highlighted. But it only became clear with the completion of this commentary that in addition to the pseudo-and deutero-Pauline letters (especially Colossians, Ephesians, and 1 Timothy) Hebrews, and the letters ascribed to Peter (1 Peter), all seven of the authentic Pauline epistles, the Synoptic Gospels (especially Matthew), and possibly Revelation had all exercted a quite surprising influence in the shaping of the Odes of Solomon''. All that, and yet there is not one quotation or clear allusion from any of those texts in any of the Odes!
[...]
Professor Lattke is mistaken when he reasons from the similarities he finds between one set of documents and another that one set therefore pre-existed and exerted a causal influence on the other. I see no reason to conclude from ideological and phraseological similarities that a whole host of New Testament texts ''exerted a quite surprising influence in the shaping of the Odes of Solomon''. On the contrary, I think it is much more likely that the Odes of Solomon exerted quite a surprising influence in the shaping of the New Testament. I mean only that ideas and phrases found in the Odes of Solomon wer written before the time when similar ideas and phrases were written into the New Testament, and the community behind the Odes of Solomon was in existence before there were any Christian communities oriented to Jesus of Nazareth. I have no reason to believe that any New Testament author had read any of the Odes, or that any author of the Odes had ever read any of the New Testament.
The Odes of Solomon, I believe, came first; the writing in the New Testament was later, perhaps a generation or two later, I believe that the ancients who placed the Odes of Solomon alongside the Psalms of Solomon and who included both the texts in their lists of Hebrew Bible apocryphal books had it right. I believe that the reason Jesus of Nazareth is not known by name, or by quotation, or by deed, or by stories of crucifixion and resurrection anywhere in the Odes of Solomon is because they were written before the time of Jesus' ministry. I think that the Odes come from the period 50 B.C.E. - 25 C.E., roughly the time that many of the Dead Sea scrolls were produced and not far from the period that is commonly assigned to the Psalms of Solomon.
(p. 270-271)
ARGUMENT FROM THE SAME TYPE OF SPIRITUAL POSSESSION EXPERIENCE:
To experience, as Odes 32 puts it, ''light from Him who dwells in them'' or to receive the glory that God gave to Jesus, as John 17:22 phrases it, cannot be two different things from two unrelated forms of first century Judaism. They are, I think, substantially and essentially the same thing. But while the Gospel of John focuses on Jesus of Nazareth, the Odes never do. Therefore, I think, the Odes came first and then Jesus, and then Paul's Gospel, John's Gospel, and the religion of Christianity.
(p. 281)
David Aune believes that the Odes of Solomon are the sort of hymns Paul describes with the term odai pneumatikai or ''spiritual songs'' in Col. 3:16 and that ''a member of the Pauline circle connects this term even more closely with inspired utterance: ''Be filled with the Spirit, addressing one another in psalms andhymns and spiritual odes'' (Eph. 5:18b-19). He believes that such odes were sung during ecstatic congregational worship...
(p. 266)
ARGUMENT FROM THE COMMON EXPERIENCE OF PRE-PAULINE PERSECUTION:
In the Odes of Solomon we may hear the feelings of those who were persecuted by the likes of Paul. For example, in Ode 28 the speaker says,
(p. 275)
When God revealed his son in Paul the first thing Paul did was to go to Arabia. [...] This does not indicate to me that Paul had any significant interest in Jesus' life or teaching, quite the opposite. [...] Bear in mind that all Paul knows of Christianity at this point is antagonistic information that supports the view that it should be persecuted. That is not nothing; people who persecute movements have some idea of what it is they are persecuting. But if the network of churches that Paul persecuted was based on the life and teachings of Jesus of Nazareth and if God revealed His Son in Paul so that Paul now affirmed that he persecuted the true Churches of God, he would have gone first to Jerusalem, or Capernaum, and not to Arabia. However, if the Odes represent a form of Christianity without a focus on Jesus, then Paul could begin to preach what he formerly condemned without thinking that he needed to find out more about Jesus. In that case, though, what would motivate Paul to speak so fervently about Jesus Christ and him Crucified? Paul clearly separates two things we put togheter. About the life, personality, miracolous deeds and wise inspired saynings of Jesus he evidently cares nothing of all. He seeks no information about such things and nothing about them is ever mentioned in his letters, but about Jesus the crucified and risen Christ he cares a great deal.
(p. 276-277)
Davies appeals also to arguments shown by Jack T Sanders,
The New Testament Christological Hymns: Their Historical Background, Cambridge UK 1971. Sanders puts the Odes in pre-Christian Judaism because his authors shared the same old myth of the ''redeemed redeemer''. A clue of this is that the term ''Lord'' found often in the Odes comes from another religious tradition than Judaism, the worship of Adon/Tammuz. And not coincidentially, Paul was operative in Damascus and Antioch.
David Aune writes, in connection to Ode 38:1 specifically [...] that the mention of a chariot within a context where a trip to the celestial Paradise is in view calls to mind Gershom Scholem's claim that Paul's use of the term 'Paradise' in II Cor. 12:3 togheter with an experience of mystical transport puts the apostle of the Gentiles in the tradition of Jewish Merkabha (''Chariot'') mysticism. The Antiquity of this variety of Jewish mysticism is attested by the discovery of the socalled Angelic Liturgy (4QS1) at Qumran...
(p. 262)