I would write to the archive of the "Offizialat Vechta". They have all the parish records of the Roman Catholic parishs of the region Oldenburger Münsterland. In the other regions of Oldenburg you can find only a handful RC. The contact is archiv@bmo-vechta.de. But the spelling of the name also could be Heidmann.
But your ancestor also could have born in the region south of Essen around Quakenbrück. This region was a part of the former kingdom of Hannover. If you could find the person in Vechta, you can write to the OSFA, the genealogical society for the region Osnabrück where Quakenbrück belongs to. The address is post@osfa.de.
Good luck!
Gunter (Jüchter)
P.S.: If your ancestor came from the Oldenburg region I would be proud to present him with his family on our page www.auswanderer-oldenburg.de.