I'm a Canadian citizen and as part of a RTW trip next year I am booking a flight from Cairo to Lagos, Nigeria, and the cheapest flight has two connections, 1) in Karhtoum, Sudan and is a 45 min layover, and then 2) in Addis Ababa for another 45min. Would I need to apply for transit visas for either of these countries before flying out?
In general you don't need transit visas when just making use of the airport in a country, as you don't go through passport control/customs at all.
You only need one if you want to stay in the country and your passport is stamped.
Transit visa requirement varies, often depending on the duration of transit and nationality. Nonetheless, having said that, given the information you've provided, you won't need transit visa for both Sudan and Ethiopia.
Sudan: transit visa not required for duration less than 6 hours
Ethiopia: transit visa not required for duration less than 12 hours
One website that I found very useful in checking for visa (and vaccination) information is:
The site aims to provide as most up to date information as possible, and if you still have any other doubts, no harm double checking with the nearest embassy of your destination countries for further clarification.