So I'm way late to the discussion. For Aedra, I'd go with Julianos for education in Imperial circles. The old Nords had Jhunal who is the equivalent of Julianos and is also a Hearth God. However note that Jhunal seems to be out of favor and is currently absent from modern Nord worship. For Daedra, that's a bit tough because the daedra are selfish and so don't really share well... including sharing knowledge. Hermaeus Mora hordes knowledge but doesn't really teach (sort of trades a bit), so he doesn't exactly fit what you described. But since you want both knowledge and strictness... I gotta go with Jyggalag, Daedric Prince of Order, Logic and Deduction. His great library was said to contain a logical prediction of every event or action that would ever take place in Mundus. For strictness, you aren't going to find anyone to top Jyggalag.

My take: Akatosh: According to UESP, he "embodies the qualities of endurance, invincibility, and everlasting legitimacy while promoting the virtues of duty, service, and obedience." Julianos would work better for straight up education, but since you want to emphasize strictness, I would say Akatosh's focus on duty and perseverance is more what you're looking for. Peryite: Also known as the Taskmaster. Not really any good choices among the Daedric Princes, but he's the closest I guess.

Let's talk about education. Strict education. Explicitly including spanking to discipline absentminded students and enhance the lectures. Now, the question comes up, which aedra and which daedra would be MOST pleased with such an education? Like Zenithar is considered the god of trade, which would be the aedra/daedra god of strict education? And why? ? Whose shrine would the head mistress/master have in the main hall of such an educational institute? Mind you, that I am NOT asking about slavery, whipping, brutality, rape , etc...! Please vote and explain your opinion below. Thank you.