In the name of Allah, Most Gracious, Most Merciful.
Wa alaykum assalam wa rahmatullahi wa barakatuh.
The majority of scholars from amongst the companions of the Prophet (peace be upon him), and their successors who came after them, from amongst both the scholars of hadith and fiqh, were of the opinion that it is impermissible for one in the state of impurity to recite the Qur’an. They based their opinion on evidences, the most exemplary of which is that related by the five (books of hadith), by way of Shu`bah, from `Amr bin Murrah, from `Abdullah bin Salamah, from `Ali (may Allah be pleased with him), that he said, “The Prophet (peace be upon him) used to come out of the toilet and teach us Qur’an and eat meat with us, and nothing used to separate him from the Qur’an other than sexual impurity.”
This hadith has been discussed regarding [the status of the narrator] `Abdullah bin Salamah and that his [precision of] memorization changed. So Ahmad and others classify it as weak. As for Tirmidhi, Ibn al-Sakan and `Abdul-Haqq al-Shibli, they classify it as authentic.
There are a group of scholars who allow the one in a state of sexual impurity to recite the Qur’an for lack of evidence prohibiting it. This has been narrated from `Ibn Abbas (may Allah be pleased with him) and Ibn al-Musayyib, and it is the opinion of Dawud al-Dhahiri and Ibn Hazm, as well as the madh'hab of the Dhahiris and the preferred opinion of Ibn al-Mundhir.
As for Tasbih and all other utterances of remembrance, then there is nothing to prevent one in a state of sexual impurity, or others, from uttering in oneself or audibly. Tirmidhi said, after discussing the majority opinion of not allowing one in a state of sexual impurity or menstruation from reciting the Qur’an, “The one in a state of sexual impurity and the menstruating one has been permitted to utter Tasbih and Tahlil [utterance of la ilaha illa Allah].”
Furthermore, the consensus allowing that has been stated by Nawawi in al-Majmu` Sharh al-Muhadhab (2/189), as well as at the beginning of his book al-Adhkar.