Combining two of the theories on
tvtropes regarding the nature of the cast of
Father Ted, I propose the following:
Father Jack was a Soldier of Heaven, who was terribly mauled in Ethereal combat, developing a number of Discords (Lustful, alcoholic, Angry), and ultimately lost an Ethereal Force, leaving him the surprisingly spry (high Corp Forces) human wreckage we see living in the Parochial House. Father Dougal is an Impudite, probably of Nightmares, who is there to keep hammering on Jack. Ted is exactly what he seems to be, a less than competent priest with a gambling problem, and Dougal periodically engineers the destruction of his dreams and the fulfillment of his nightmares because he's a demon of Nightmares, and that's what he does. Mrs. Doyle would be a deeply incompetent angel (possibly Reliever), who's there to see to Jack, has no previous
Corporeal experience and only does what she was specifically told was part of her Role, and is so bad at her job that she has utterly failed to suss out a clue about Dougal's nature.