"Awfully" originally was so spelt only to distinguish it from "aweful", and meant "awe-inspiringly". There's a passage in a First World War book [Dunsany's collection Tales of War [?], long out of print]:
The night was awfully still. I use the word not as Private Smith would have used it.
But,like so many adjectives, the meaning was gradually chipped away, by Private Smith among others, to mean very.
Did you mean the process by which slang reduces everything to either very or good/ bad (or sometimes both)? Or the inevitable result of this, by which "perfectly awful" and "awfully perfect" become opposites? If the second, I think it's too transient to have a name, since hardly anybody now uses either phrase, and no doubt when one of them becomes fashionable slang in twenty years the meaning will be different again.