I presume you are searching for a list of Louisiana residents who took the Oath of Allegiance to the United States during the war. Since there were no responses here from anyone who has seen such a list, I recommend you contact the National Archives and pose the question there. Be sure to let us know what you learn.
You should expect to find a record of any Oath of Allegiance taken by a Confederate soldier while the war was underway, or during the final phases of shutting down the war (April 1865 through July 1865), in the Compiled Military Service Records for each individual soldier.
Relative to an Oath of Allegiance to the Confederate States, public office holders were required to take such an oath. I don't have an example at hand, but it would have been identical to the United States oath of office for public officials, substituting "Confederate States" for "United States".
The enlistment oath taken by all Confederate soldiers contained wording that includes a statement of allegiance to the Confederate States.
John asked: >>>Is it true Confederate soldiers who were discharged during the war and sent home had to take the oath?<<<
Confederate soldiers who were released from service during the war by the Confederate army were not required to take an Oath of Allegiance to the United States. They had already taken an oath to serve the Confederate States when they enlisted. Only if their homes were in areas under Federal control would they have faced the necessity of taking an Oath of Allegiance to the United States in order to go and remain there for any length of time while the war was going on.
John asked: >>>Were residents of New Orleans required to take the Oath during the occupation or else be arrested and sent off?<<<
Yes.
Initially, in June 1862, residents of New Orleans were given the option of taking an Oath of Allegiance to the United States, or if claiming foreign citizenship, an oath of neutrality. Passage of the Federal Confiscation Act and its signing by President Lincoln on 17 JUL 1862 opened the door to the seizure of property of "disloyal" residents. General Butler added this to his program in September 1862.
See Department of the Gulf General Orders No. 76 dated 24 SEP 1862 (OR, I, Volume XV, pp575-6), General Orders No. 82 dated 17 OCT 1862 (OR, I, Volume XV, p581), and memo from Brigadier General T. W. Sherman, commanding the Defenses of New Orleans, to Lieutenant Colonel Irwin, Assistant Adjutant General, Department of the Gulf dated 28 MAR 1863 (OR, I, Volume XV, p696).
Hugh Simmons