MAD was originally a regular sized four-color comic book. This particular issue has a parody of George MacManus' comic strip BRINGING UP FATHER, guest starring Marie Wilson as MY FRIEND IRMA from the radio show of the same name. MAD would frequently mix up characters like this, although much of the story follows the conventions of the original comic strip fairly closely, at least until they have the story take a supposedly more serious slant with the idea that that is supposed to be funny. Actually it's a little too horrible to be funny, something that was frequently a problem with MAD.
The blonde girl is supposed to be "Irma", a character played on the radio by Marie Wilson on MY FRIEND IRMA.
The guy with the hat and the big nose is "The Shadow", from another radio show. Irma is shown taking "Ends" because that was a sponsor of radio's MY FRIEND IRMA.