Basically, Oscar (and that of his species, according to one Muppet designer when being asked to describe them), is made up of not just grumpiness, but also fun. These words best describe him: grumpy, hilarity, cheeky, messy, naughty, sarcasm, silliness...add up alll these and that's what you get. But yeah, overall, there's goodness.
Which is what you have to understand when you're writing for him. You'd have to think backwards---like Opposite Day.
You know, being miserable from being happy, which drives one miserable, then happy; liking to be left alone, but only to realize that if left alone, then he'd have no one to be grouchy with, Something that'd be yucky would be "good", etc.
And, the Muppets on the street were "kids", and the humans (adults) would be there to teach them, help them with certain things in life, and most of all, be the butt for all their little shenanigans.
There were times that the Muppets drove each other insane, there were times that they'd hurt another's feelings, make mistakes, etc. But hey, they'd always manage to work out in the end.
I think he crossed the line on Christmas Eve on Sesame Street. He was very mean to Big Bird.
Okay, I thought I'd admit this to everyone---you may not agree, but I think it's best that I share it: the real reason, why Sesame Street went downhill was...that special. I'm serious. You know, SS was like this show filled with all that "warm, nurturing comedy" and that of which makes it almost like a Laugh-In type of show. But after that happened, it didn't feel like it anymore. At least, just not as much. Plus, it kinda broke the "thinking backwards" rule.
Just thought I'd say that.