I'd like to provide you with these links :
drink - Definition from the Merriam-Webster Online Dictionary
oblivion - Definition from the Merriam-Webster Online Dictionary
I could not find the definition for "drink oneself into oblivion."
Perhaps it could mean..."to drink so much that sb can't remember anything."
I'm not a native speaker of English, so please forgive me if I'm wrong.
Student or Learner