His overwhelming power stems from the Cursed Seal of Heaven that Orochimaru inflicted on him. While we see the curse mark causes him pain, he is able to use it to drastically increases his power.
The Naruto Wikia notes this:
Like all cursed seals, the user receives increased chakra levels and physical capabilities when the seal is active, to the point where with the second level, Sasuke was equal in power to Naruto's one-tailed form when he first used it.
There is no monster inside of Sasuke, nor a tailed beast like the jinchuuriki. The transformation is caused by activating the second level of the curse mark.
When Sasuke activated the second level of the seal, his skin turned dark-grey and his hair grew and turned dark blue. His eyes also turned dark grey. Additionally, he grew webbed-claw-shaped wings from his back which he could use to fly and glide, and a dark, star-shaped mark appeared across the bridge of his nose.