The position of all four schools of Sunni Islam is that it is not permitted for someone without wudu to touch the Qur’an. Allah Most High says,
“None shall touch it except the pure.” [Qur’an, Surat al-Waqi`a: 79]
And in a famous hadith, the Prophet (peace and blessings be upon him) instructed Amr ibn Hazim that, “None is to touch the Qur’an except the pure.”
Ibn Abd al-Barr, the great Maliki jurist and hadith master, said that this is a ruling regarding which the recognized scholars of fiqh–the four major mujtahid imams and others–have scholarly agreement regarding. [Ibn Abd al-Barr, al-Istidhkar, 2.472; Qurtubi, al-Jami` li Ahkam al-Qur’an, 17.193] The position to the contrary is erroneous, and unbefitting the respect and veneration due to the Qur’an.
In general, it is permitted to recite the Qur’an (without touching it) when one is in a state of minor ritual impurity.
It is superior, when reasonably possible, for one to do wudu.
In a state of major ritual impurity, it is not permitted to recite the Qur’an. [Ala’ al-Din Abidin, Gifts of Guidance]
And Allah alone gives success.