Punishment is middah k’middah, “measure for measure”. The sin of strange fire was punished by them being consumed by fire.
Aaron was obviously aghast, but kept his dignity. Vayyidom Aharon, “And Aaron was silent” (Lev. 10:3).
Nachmanides makes the suggestion that Aaron did first cry out with a loud cry of anguish, and only then did he fall silent. Was Aaron crying out against God? Was he crying out because of the effrontery of his sons? Was it a possibly primitive cry at the shock of the moment?
Whatever the nature of the cry, all commentators agree that he did not speak because he could not. There are times when words only cloud the situation, times when silence is the only thing to say.