@GodfatherPartTwo summed it up well. Rabbinic Judaism (Talmud & Zohar) despise Jesus, while Islam attempted to establish its own legitimacy by copying and editing anything and everything they could get their hands on. Neither accepts Jesus and the Trinity.
If anyone is interested, below is more in-depth analysis. Unlike the Quran, the Talmud has some very blasphemous passages, so I have not provided direct quotes.
On Jesus' ascension to Heaven:
Judaism
As far as I know, no references of ascension in either the Talmud or the Zohar.
Islam
The Quran, Surah An-Nisa (4), 157-158: "... for boasting, 'We killed the Messiah, Jesus, son of Mary, the messenger of Allah.' But they neither killed nor crucified him—it was only made to appear so. Even those who argue for this crucifixion are in doubt. They have no knowledge whatsoever—only making assumptions. They certainly did not kill him. Rather, Allah raised him up to Himself. And Allah is Almighty, All-Wise."
On Jesus as the Messiah:
Judaism
The Talmud, Tractate Sanhedrin 98a: "The son of David [i.e., the Messiah] will not come until the Temple is rebuilt."
The Talmud, Tractate Sukkah 52a: "Rabbi Yehoshua ben Levi said: The son of David will come only in a generation that is either entirely righteous or entirely wicked... if they are righteous, he will come with the clouds of heaven; if they are wicked, he will come as a poor man riding on a donkey."
Maimonides, Mishneh Torah, Hilchot Melachim 11:4: "If a king will arise from the House of David who delves deeply into the study of the Torah and observes its mitzvot as prescribed by the Written Law and the Oral Law, and he will compel all of Israel to walk in [the way of the Torah] and rectify the breaches in its observance, and fight the wars of God, we may, with assurance, consider him the Messiah... If he succeeds in the above, builds the Temple in its place, and gathers the dispersed of Israel, he is definitely the Messiah."
Based on such texts, they conclude that Jesus was not the Messiah, as the specified conditions were not met.
Islam
The Quran, Ali 'Imran (3), 45: "Remember when the angels proclaimed, O Mary! Allah gives you good news of a Word from Him, his name will be the Messiah, Jesus, son of Mary; honoured in this world and the Hereafter, and he will be one of those nearest to Allah."
On Jesus' soul and body in heaven:
Judaism
The Talmud, Tractate Gittin 57a:1-4. I do not wish to quote this. You may look it up yourself, if you'd like.
Islam
The Quran, Surah An-Nisa (4), 158: "... Rather, Allah raised him up to Himself. And Allah is Almighty, All-Wise."
On Jesus' return:
Judaism
Jesus is not considered the Messiah, therefore not expected to return.
Islam
No direct mentions in The Quran that I'm familiar with. The vast majority of interpretations come from the Hadith, which itself is slightly different between the various Islamic sects and traditions. Imam Mahdi and the return with Jesus is mentioned in both Sunni and Shia Eschatology. There is just too many Hadith.
On Jesus coming of virgin birth / his divinity:
Judaism
The Zohar, Parashat Vayechi, Section 1, Verse 212a: "The Messiah, who is the central column, is a human being, the son of a human being, and he is clothed in the garments of the Torah."
They conclude that their Messiah will be a human with no divine attributes.
Islam
Yes on virgin birth:
The Quran, At-Tahrim (66), 12: "There is also the example of Mary, the daughter of ’Imrân, who guarded her chastity, so We breathed into her womb through Our angel Gabriel..."
There are many other references. As a matter of fact, an entire Surah is devoted to Mary (Surah Maryam, 19). That Surah draws heavily from the Gospel of Luke. There are also other readings from the Infancy Gospel of James and the Infancy Gospel of Thomas.
No on divinity:
The Quran, Ali 'Imran (3), 59: "Indeed, the example of Jesus in the sight of Allah is like that of Adam. He created him from dust, then said to him, 'Be!' And he was!"
Here they explicitly go against the Trinity:
The Quran, An-Nisa (4), 171: "O People of the Book! Do not go to extremes regarding your faith; say nothing about Allah except the truth. The Messiah, Jesus, son of Mary, was no more than a messenger of Allah and the fulfillment of His Word through Mary and a spirit created by a command from Him. So believe in Allah and His messengers and do not say, 'Trinity.' Stop!—for your own good. Allah is only One God. Glory be to Him! He is far above having a son! To Him belongs whatever is in the heavens and whatever is on the earth. And Allah is sufficient as a Trustee of Affairs."
The Quran, Maryam (19), 36: "Jesus also declared, 'Surely Allah is my Lord and your Lord, so worship Him alone. This is the Straight Path.'"
On Jesus' Miracles:
Judaism
The Talmud, Tractate Sanhedrin 43a:20-22. Again, I do not wish to quote this. Suffice it to say that it says the miracles were done by sorcery and idol worship.
Islam
The Quran, Ali 'Imran (3), 49 "... ‘I have come to you with a sign from your Lord: I will make for you a bird from clay, breathe into it, and it will become a real bird—by Allah’s Will. I will heal the blind and the leper and raise the dead to life—by Allah’s Will. And I will prophesize what you eat and store in your houses. Surely in this is a sign for you if you truly believe."
The "bird from clay" is a direct copy from the non-canonical Infancy Gospel of Thomas.