British Rule: When the British took control of Nigeria around the mid Nineteenth century, a large scale rural-rural immigration occurred, due to the fact people were moving from areas with less jobs, to areas rich in natural resources where many factories and oil rigs were located. The British needed a work force for the plantations, mines, and public transportation systems as well.
Also, rural-urban migration occurred, as people began to move to busier cities such as Lagos, Kano, Zaria, Enugu, Ibadan, Sokoto, and Kaduna. The important reason this came about was improved connections through railways and public transportation between major cities.
As for International immigration and emigration, people often moved to Nigeria because of being under the French's (who were said to be more oppressive) control. Many moved out of Nigeria due to over all poor living conditions, as many people were still living in poverty, despite the job availabilities.
Migration since Independence:
After Nigeria's independence in 1960, there was a large scale emigration to the UK, as well as other European countries. Much of this emigration was students moving to get a better education, and professionals moving to have better working conditions. Many high skilled nurses and doctors were recruited from Nigeria to Saudi Arabia and other Gulf States. Thus, Nigeria experienced massive brain drain prior to it's independence.
Internal Migration prior to Independence:
After Nigeria's independence in 1960, the government reorganized Nigeria from 3 regions into multiple states, to enhance internal migration. When the military run government made Abuja the capital in 1991, 200,000 workers relocated from Lagos (the old capital) to that area for more job opportunities. It's population jumped from 378,671 people to 778,567 people in merely 15 years, making it the fastest case of urbanization in West Africa.
The country's South West area, including its most populous city Lagos, attracts people from all over Nigeria. This region hosts Nigeria's 2 main ports, 65% of it's industrial plants, and large agricultural plantations. However, it is such an attraction that this area, especially the city of Lagos, has become grossly overpopulated, hurting many of the residence's daily quality of life with cramping and pollution.
Internally Displaced Persons:
Due to some political unrest and conflicts in Nigeria, there are many internally displaced persons who have been forced to move and take refuge in cities in Nigeria other than the one's by which they originate. About 480,000 people were internally displaced between 2006 and 2008. The main reason for these IDPs was disagreements and clashes over oil exploitation and exploration in the Niger Delta, which flows through a bit of Nigeria.