These verbs mean to bring to a natural or proper stopping point. Complete and finish suggest the final stage in an undertaking: "Nothing worth doing is completed in our lifetime" (Reinhold Niebuhr). "Give us the tools, and we will finish the job" (Winston S. Churchill).
Close and end both imply bringing something ongoing to a conclusion: The band closed the concert with an encore. We ended the meal with fruit and cheese. End can also mean putting a stop to something, often with finality:"Many advocates say [putting] laptops in schools is a promising way to end the digital divide between the races"(Char Simons). "It left him more exposed than ever, forcing him to end the career he loved" (Molly Worthen).
Conclude is more formal than close and end: The author concluded the article by restating the major points. Terminate suggests reaching an established limit: The playing of the national anthem terminated the station's broadcast for the night. It also indicates the dissolution of a formal arrangement: The firm terminated my contract yesterday.