The No. 1 definition of "dreadfully" according to OED (Oxford English Dictionary) is "extremely or very much," as in "you're dreadfully thin" or "I'm dreadfully sorry!" or "I'll miss you dreadfully."
The second definition of dreadfully, "very badly," doesn't apply of course because of grammar. You can't have "very badly" fun. Grammatically you could have "very bad fun," but that would be "dreadful fun," (although that wouldn't make sense).
Umm... no?
No, it's not really an oxymoron at all.
The No. 1 definition of "dreadfully" according to OED (Oxford English Dictionary) is "extremely or very much," as in "you're dreadfully thin" or "I'm dreadfully sorry!" or "I'll miss you dreadfully."
The second definition of dreadfully, "very badly," doesn't apply of course because of grammar. You can't have "very badly" fun. Grammatically you could have "very bad fun," but that would be "dreadful fun," (although that wouldn't make sense).