Comic strips seem to function as they do because of an implied set of rules that become established. Readers of the comics each form their own opinion of what these rules contains. Perhaps I can better express this concept by giving some examples...
1. Charlie Brown will never kick the football.
2. Andy Capp will never get a job.
3. Ignatz Mouse will always find a way to bean Krazy Kat with a brick.
4. Gyro Gearloose will always be lucky.
I don't recall any of these rules being explained within these comic strips, but they became obvious to me by reading the comic strips over time. If the humor in a comic strip is character-driven, the characters must be consistent, thus the rules become established.
I too, am learning these rules that make "Don't Tell Grandma" function. I'm not going to explain the rulea or list them, but if you scroll down through the pages posted on this site, you'll figure them out for yourself. You'll "get it".
By the way, I have removed the Dagbo Dog comics from this website. I have other plans for that comic book stuff. I think that this website "Bob Lilly's Comics and Stories" is better suited for short form works, like the Grandma comic strip.