I know what happened as per puranas , but does Mahabharata also mentions the same or different? How andhaka had taken birth, did he wanted to be husband of goddess parvati? At last how the war happened between them?
The story of andhak is described in Mahbharat Harivamsa parva Chapter 86
VaishampAyana said Long ago, after her sons were slain by Vishnu, the splendorous Vishnu, Diti worshipped Kashyapa, the son of Marichi, by doing penance. O the one of bharata race! Diti performed penance, appropriate to various times and served, obeyed and treated the sage sweetly. Then Kashyapa was pleased. The one with the wealth of penance (Kashyapa) told her: O good one! I am pleased with you. O the one who is fixed in penance! Ask for a boon. O lord! O the best among those who observe dharma! The devas killed my sons. I desire to have a highly valiant son who cannot be killed by the devas. O the daughter of DakSha! O goddess! You shall have a son who cannot be killed by the deva-s. O the one having eyes beautiful as lotus! There is no doubt in this, but leaving Rudra, the true lord of deva-s (except Shiva, no other deva will be able to kill him), because I have no power on him. Hence your son shall always protect himself from him (lord Shiva). (VaishampAyana said: O Janamejaya!) Saying this, kashyapa, who speaks the truth, touched the belly of goddess (diti ) with his finger. Then she delivered a son. O the son of kuru! (janamejaya! vaishampAyana continued) He had one thousand arms, one thousand heads, two thousand eyes and that many number of legs. O the one of bharata race! Even though he was not blind, he behaved as if he was blind. Then those who reside there, called him by the name Andhaka.
He started spreading terror.
The one with wicked intellect (andhaka) broke the trees in the forest and destroyed gardens. He took away by force, the horses, sons of uchchaiHshravaH (divine horse) from heaven. O the one of bharata race! (O Janamejaya! VaishampAyana continued) (Andhaka), proud due to the boon, took away forcefully, the divine elephants, sons of the elephants of directions, as the deva-s were watching. The wicked soul, the thorn of deva-s, created obstacles to those who satisfy the deva-s with sacrifices and penance.
Andhaka reached to fight with Lord Shiva.chapter 87 of Harvamsa parva
O the one of bharata race! andhaka heard the words of nArada and understood the meaning. The great asura (andhaka) mentally decided to go to the mountain of mandara. The one with great power (andhaka) assembled demons of great splendor. The angry demon immediately went to the mountain of mandara, the residence of the great deva, shiva.
Lord Shiva killed Andhaka.
The lord released his spear, having splendor as blazing fire. That terrible spear struck on the chest of andhaka. It reduced the terrible demon Andhaka, a thorn for the good people, to ashes. Then the groups of devas, all the sages having wealth of penance praised and pleased ShaNkara (Shiva) as he killed the enemy of the world.