This is a lengthy comparison which came recently by request. Some of these words tickle my legal fancy; others just seem interesting for whatever subtle distinction they may yield. Here goes...
Exculpatory v. Excusatory v. Expiatory
Exculpatory is an obvious legal word ("exculpatory evidence" in litigation or "exculpatory clause" in contracts being among my favorite phrases), and means "tending to clear from charges or guilt", directly from the Latin ex-culpare (out of blame). Excusatory just means serving as an excuse, which is unhelpful, but "excuse" means to release from duty, guilt, obligation, etc., from the Latin excusare for "to put outside" or "release" as from such duty, guilt, obligation, etc. So there is already a distinction in the person and the act in that a third-party will excuse a wrong, while a neutral thing (a document or testimony of a person) may exculpate an individual. Finally, expiatory means to "atone, make amends or reparation", deriving directly from expiare ("to make good"), which vests with the wrongdoer and implies greater action by the wrongdoer than merely asking for forgiveness. There is an putative reference to a moral sin by the definition of "atone", but this is incorrect. Expiate and atone are not synonyms, and cannot ascribe meaning interchangeably. So while there may be an overlap in these words generally, the person or thing doing the releasing and extent to which action is required to release, i.e., implicity (by the evidence), by word or act of acknowledgment (by forgiveness or by restitution), are the critical difference. The defendant's excusatory statement that he 'wasn't there" at the time of the crime was not credible until the exculpatory evidence of the missing security video tape proved his whereabouts, and provided a sufficient alibi, but neither the statement nor the video tape were expiatory for the defendant's conduct during the trial when he beat up his counsel, breaking her arm. Except for exculpatory, I think I prefer excusatory and expiatory as verbs (which I'll get to presently). The evidence of his brother's habit for "borrowing" his gun while he was sleeping tended to exculpate him from being responsible for the "accidental" shooting of the neighbor's dog. I suppose the only fun you could have with this is to use it outside the criminal context for which it is intended. Such as, if there is a particularly damning tort issue. Bringing his wife breakfast in bed, taking out the trash, and doing all the laundry, exculpated him for forgetting her birthday.
Accusatory v. Admonitory
This pair was lumped in with the prior trio, but on first blush, these are distinct since these words create the blame which is being released with the above words. Accusatory derives from accuse which means "to call to account" (and shares a common origin with excuse from "cause" meaning "reason, sake, or case"). Admonitory is a warning of current or past wrongdoing, from the Latin monitorius for "reminding or warning". The prefix "ad" has a directional inference, but could just mean "near" in this instance. Which makes admonitory less damning than accusatory, but again, both are better as verbs. My admonitory glances to make the children stop squirming go largely unnoticed, and my accusatory huffs of disgust are equally ignored by their parents. This doesn't really work too well. I admonish small children to stop squirming during movies, but I accuse their parents of failure to control their children. Much better! Plaintiff's counsel received admonitory advice from the judge to "move it along" with the witness and an accusatory glare from Defense counsel for wasting time. Again, it's correct, but it doesn't really convey the full meaning. The judge admonished Plaintiff's counsel for wasting time with this witness, and Defense counsel chimed in with a withering eye-roll accusation.
I think the only thing to be gain from using any of these words as adjectives is the emphasis for using what are otherwise known and used words in this unusual form. So, to expand an adage, choose and use your words carefully!