Marina said the same thing, about Oswald telling her, "I shot Walker", in both her WC and HSCA testimonies.
As to his post-assassination emotional state:
Johnny Brewer: "He [Oswald] just looked funny to me. Well, in the first place, I had seen him some place before. I think he had been in my store before. And when you wait on somebody, you recognize them, and he just seemed funny. His hair was sort of messed up and looked like he had been running, and he looked scared, and he looked funny."
Mary Bledsoe (on the bus Oswald got on): "And, after we got past Akard, at Murphy---I figured it out. Let's see. I don't know for sure. Oswald got on. He looks like a maniac.... That is---I was just---he looked so bad in his face, and his face was so distorted..."
As Norman Mailer pointed out in his book about Oswald: "We have seen him become hysterical on one occasion and, on another, be the coolest man in the room. If we have come through the turnings of this book without comprehending that the distance between his best and worst performance is enacted over a wide spectrum, then we have not gained much."