I would like to know if Muslims are allowed to cutting hair and nails when major impure (Junub)?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. Actually we do not see any legal prohibition to clipping nails or cutting hair while in a state of ceremonial impurity. But it is prohibited to shave the beard according to the opinion held by the majority of jurists of the Salaf (first righteous generation of our Ummah) as well as the latter ones. This prohibition is the same whether during the ceremonial impurity or otherwise. For more details on the ruling of shaving the beard, you may refer to Fatwa: 81533. Allah knows best.