In classical Latin, oro usually means "I request" and is transitive. Usually it takes two objects, the person asked and the thing requested, though one can be omitted if it's clear from context. (When used intransitively, oro usually means "I orate".)
In ecclesiastical Latin, oro takes on the more technical meaning of "I make a prayer" or "I am engaging in prayer" in the specifically religious sense, and when it does so, it's usually intransitive. At least, it isn't necessary to specify the thing requested, since the prayer doesn't have to be a request. But when ecclesiastical writers want to specify or imply a thing requested, they can still use the verb actively, just like classical writers.
In the two examples you gave without ad, the thing requested is stated immediately beforehand, so the classical transitive sense seems appropriate, with the request implied.
However, it's not always correct to make a sharp distinction between the two constructions. For instance, in the Vulgate, you can find both "oravit ad Dominum, dicens" and "oravit Dominum, dicens." I see no reason to press a distinction in that case.
