Waste disposal/recycle 

I have an amount of paper, some sensitive some not. Where can I dispose of it in this area accordingly?

can anyone give waste management/recycling companies that are willing to do business in Nigeria 

Shred it first! 

I would recommend you to buy a home shredder so that your sensitive documents are safe and then you can recycle that paper at your local recycling bank along with the rest of your paper.