Question: Why does Gary Oldman speak with a Russian accent when Lee Harvey Oswald was from New Orleans?
Question: Was the head movement argument to the jury verbatim from the transcript of the actual trial of Clay Shaw?
Answer: No. The argument which mentions was the first closing argument by an assistant to Garrison and in it he mentions "back and to the left" once but not the multiple statements shown in the movie. The actual transcripts are available on line.
Answer: Lee Harvey Oswald was very sympathetic to the communist ideal, and lived in Russia for a while. He probably adopted the accent as an affectation towards that end.
Grumpy Scot