From Dave Tweed (moderator), in a comment:

[...] I went ahead and deleted the questions. They weren't great questions to begin with, and there's nothing wrong with the OP wanting to delete them. The problem is that if a question has any up-voted or accepted answers, the system won't let him do it himself, so a moderator must handle it. He should have flagged them rather than vandalizing them, but low-rep users can't really be expected to know that.

And from Nick Alexeev (moderator), also in a comment:

I took a liberty to undelete the question (and lock it against vandalism).

So the answer seems to be: raise the issue to a moderator's attention and let them handle it as appropriate.