Although a number of Nigerian languages have been and are written to some degree using the Arabic script or Ajami, the Latin script was adapted for major languages (notably Hausa, Yoruba, and Igbo) in the 19th century and promoted in the colonial ands post-independence periods. Its use is thus widespread and more or less standardized for at least the major languages.
This page will deal mainly with efforts to define the standardized orthographies on a countrywide basis. For the history and curent state of orthographies for specific languages, please see the specific language pages.
Wikipedia has some information on this. The history given there may be incomplete.
Linguist Kay Williamson published in 1984 a book on orthographies of Nigerian languages. This builds on earlier work by, among others, Ayo Bamgbose. Appendix 2 in Williamson's book (pp. 61-63) summarizes this information (scanned images are presented below). There is some question about whether these represent the orthographies currently in use (see Current trends below).
Rhonda Hartell edited a book (1993) on orthographies of African languages including data on 22 Nigerian languages. The information on Latin extended and diacritic characters from that data is summarized at http://www.bisharat.net/A12N/NIGERIA-table.htm . (See also Current trends below).
Roger Blench (personal correspondence) indicates that current usage for at least some languages may not conform with the orthographies indicated in Williamson's (1984) book. This is due in part to use of computer systems and fonts that did not accommodate certain extended characters and diacritics.
Agheyisi, Rebecca N. (ed.). Orthographies of Nigerian languages: Manual V. Lagos: Federal Ministry of Education, National Language Centre.
Armstrong, Robert G (ed.). 1986. Orthographies of Nigerian languages: Manual IV. Lagos: Federal Ministry of Education.
Bamgbose, Ayo (ed.). 1982. Orthographies of Nigerian Languages: Manual I.
Banjo, Ayo (ed.). 1985. Orthographies of Nigerian languages: Manual III. Lagos: Federal Ministry of Education.
Blench, Roger. Personal correspondence, 2006.
Emenanjọ, E. Nọlue (ed.). 2000. Orthographies of Nigerian languages: Manual VI. Lagos : Federal Ministry of Education, Nigerian Educational Research & Development Council.
Hartell, Rhonda L. ed. 1993. The Alphabets of Africa/Alphabets de Langues Africaines. Dakar: UNESCO & SIL.
Okwudishu, Appolonia U., and O.S. Salami (eds.). 2000. Orthographies of Nigerian languages: Manual VII. Lagos : Federal Ministry of Education, Nigerian Educational Research & Development Council.
Wikipedia, "Pan-Nigerian alphabet," http://en.wikipedia.org/wiki/Pan-Nigerian_alphabet
Williamson, Kay (ed.). 1983. Orthographies of Nigerian languages: Manual II. Lagos: Federal Ministry of Education, National Language Centre.
Williamson, Kay. 1984. Practical Orthography in Nigeria.
Wolff, Hans. 1954. Nigerian Orthography.