How can a Muslim repent from major sins like persistent sodomy and listening to music, especially with repeated relapses into disobedience after repentance?

Your persistence in extravagance and indulgence in desires - especially sodomy - is a grave matter. It invites Allah's wrath, and Allah punished the people of Lot with a punishment He did not inflict on anyone else.

You must turn to your Lord in repentance, for Allah's mercy encompasses all things. Allah Almighty says: "Say, 'O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.'"

You must sincerely resort to Allah, resolve not to repeat the sin, regret it, be mindful of Allah's awareness of you, and contemplate death. Know that Allah is severe in punishment.

You should accompany the righteous and frequent gatherings of remembrance, abandon bad company, and strive in supplication. For whoever strives against their soul, Allah will grant them success and aid them. Allah Almighty says: "And those who strive for Us - We will surely guide them to Our ways. And indeed, Allah is with the doers of good."