I didn't think of Nigeria as a military heavy weight but after some Google searches found some interesting things : they are 56th in numbers of total armed forces troop numbers(48th in active numbers) [ame="http://en.wikipedia.org/wiki/List_of_countries_by_number_of_troops"]List of countries by number of troops - Wikipedia, the free encyclopedia@@AMEPARAM@@/wiki/File:Question_book-new.svg" class="image"><img alt="Question book-new.svg" src="http://upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png"@@AMEPARAM@@en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png[/ame]
Alot of their equipment is older styles T-55 and such but i havent heard of their tactical doctrine / abilities. A list of the NA army deployments they seem to be able to be the rapid response team in Africa for the UN troops on the western part of the continent. Their airforce seems pretty small with 12 fighters and 24 attack planes with alot of cargo/transport planes but then again they are more than likely not going to be taking on USA/China/Russia, they look to have been in the past mostly sending out peacekeepers to other African/European(Yugoslavia) nations. Numbers arent everything though as South African numbers are smaller than that of Nigeria but the SA equipment tends to be newer, but not always as evident from their Centurians / Olifont tanks from WW2 vintage(upgraded in 1976 though) (as a side note Australia is also under NI and SA numbers wise but able to field troops far from home as well).
Forces that would be fighting in Nigeria would be at the end of relatively long supply chains exceptions being if somone like Libya decided to make a move across their souther desert, Niger's eastern desert and then attack them, which Niger would probably ask other AU countries for help, as their 5000 would be hard pressed to fight off Libya's 80k.
Egypt: Numbers of troops wise pretty large (10th overall) with modern exuipment, as far as self defence more than likely they will not be attacked by traditional forces and the only neighbor that they would likely engage in fighting with (Israel) is IMO not going to start an offencive war into Egypt (IDF has alot on its plate and not looking for more).
South Africa: Long way from any potentially beligerent country as far as having to defend their region / Africa as a whole unless the threat is from a country that is in Africa then they are more than likely equiped to handle any thing that comes their way or will be once their orders for new equipment are filled and they get proficient in its useage, the SDNAF is a long way from the SADF as far as capabilities go from my reading of some books (some fiction some not). They are the only country (so far) to give up nuclear weapons once they declared themselfs nuclear power.
In summary they seem like paper tigers until we look at who they would most likely be fighting against and then we see that they can probably hold their own vs the conflicts that they would be reasonably expected to fight.