Well, I've recently read a little bit about his life and he sounds Ti-ENTp: blunt, impatient, loved games and to act weird in parties, etc
On his intertype relations: apparently, he thought Einstein was slow and boring, although they had a good-but-distant relationship. Einstein was an idealist and Von Neumann was into war planning, for instance. ILE vs ILI? ILE vs LII?
Richard Feynman and JvN were good friends. JvN, apparently, had a hard time when relaxing and RF advised him not to take things seriously at all. Two ILEs? ILE and LIE? LIE and ILE? LIE and LIE?