I don't like the Crime and Punishment example very much. I'm not sure it is dramatic irony per se. We are witnesses to the crime of false witness, basically. The person uttering the lie knows he's lying, and we know he's lying. The fact that his victim doesn't know she's being framed doesn't necessarily make it dramatic irony.

The example from Oedipus Rex is a little complicated for a simple definition of dramatic irony. If I were to use an example from that play (and I would) I would use the speech when Oedipus swears he will catch the man who killed the late king (his father) and bring him to justice.