It would seem that Daedric Princes vary greatly in power. Sheogorath easily defeats my character, but my character easily defeats Jyggalag. My character also can't defeat Mehrunes Dagon. I would assume that Daedric Princes are widely varied in power. Am I correct?

You're confusing game mechanics with lore. Don't do this.

I do not in general, as I know much about lore, but my character still defeated Jyggalag. A mortal defeated a Daedric Prince. It sounds absurd, yet it is canon that a mortal did so and took the throne of a Daedric Prince.

A being deep in the process of mantling a Daedric prince defeated Jyggalag.

And as I alluded to in another thread speaking of measuring gods' power against each other, there's no real way to capture such a measurement.

That is true. Still, a mortal taking a Daedric Prince's title sounds unbelievable. It isn't as if my character was a daedra however. The player character is still mortal.

Since Sheogorath wanted you to be his champion, and to stop the Gray March, I think it may be possible that he gave you a bit of help, plus, if you're supposed to take up his mantle (replace him, as seems to be the case.) it would be expected that you would have some of his power by then, that's the only explanation for a mortal standing any chance against a Daedric Prince that I can think of. The fact that Sheogorath and Mehrunes Dagon seem much more powerful though could be explained by gameplay mechanics, after all, you're not meant to defeat them, you are meant to defeat Jyggalag, so Bethesda needs to make it possible to do so.

That is true.