I can do a decent Big Bird, though I tend to go back and forth between the modern day Big Bird and the relatively dopier bird of the first few years. I use that to mispronouce any surname.
My Oscar sounds like my Bugs Bunny with a scratchy throat.
I'm happy with my Grover. But I don't really try for a voice. I speak with no contractions, throw in sophisticated multisyllabic words/phrases when the time is right (You know, "A cornacopia of parts!"). It also helps to add "sir" at the end of every sentence. Usually, a voice just naturally comes in. Even if it doesn't, everyone gets it.
I can do Pepe. Similar to Grover, just add "okay" and "alright" to every sentence, and the voice naturally occurs.