The Wikipedia article seems correct in that the Dies Irae is not part of what we know as the Ordinary Form of the Mass, but it is still part of the Extraordinary Form of the Mass.
As regards the Extraordinary Form, my Missal at the
Dies Irae says that
“This Sequence is always said in the Mass on the day of death or the funeral or pro-burial Mass. It can be omitted in all other Masses for the dead.”
By “all other Masses for the dead” it seems to be referring to the traditional Masses on the third, seventh, or thirtieth day after burial, the Mass on the Anniversary, and the Daily Mass for the Dead (which can be celebrated on certain ferias, or weekdays). The words “can be omitted” is a little unclear to me; does that imply that it “can be included”?
As for November 2 (Commemoration of All the Faithful Departed), my Missal (Extraordinary Form) says that
The Sequence, Dies irae, … is said only in the principal Mass or the first Mass.
Note that in the traditional Latin Mass the Dies Irae was actually
part of the Mass. It wasn’t the equivalent of one of our hymn selections in the Ordinary Form. If you are wanting to use it in the Ordinary Form on November 2, I suppose a case could be made for using it in the place of one of the hymns, if it would have meaning for the congregation (i.e., if the congregation has some comfort level with using Latin or if a translation were provided). Or perhaps it could be used as a prelude or postlude. (I’m no expert liturgist; I’m just thinking out loud and will happily defer to someone wiser than myself.)
