Is physicist Robert Oppenheimer's phrase “Now I am become Death, the destroyer of worlds.” grammatical in English? Why not "becoming" or "now I become"?
As modern German, French, and Italian still do today, early modern English formed the perfect tenses of intransitive verbs of directed motion and some changes of state not with a form of to have, but to be and the past participle. I have become is the modern grammatical equivalent of the archaic I am become, but far from equal in rhetorical power.
This grammar change might have passed unnoticed were it not for two literary sources that both kept the form alive and gave any statement using a to be perfect tense tremendous weight: Shakespeare and the King James translation of the Bible.
I am come to know your pleasure. Measure for Measure II.4
I am come a light into the world, that whosoever believeth on me should not abide in darkness. John 12.46
Oppenheimer is quoting the Bhagavad Gita, Hindu scripture originally in Sanskrit first translated into English in 1785. While there still were English speakers using a form like "I am come" in normal speech — some of Jane Austen's characters regularly use the form — it is unlikely that the translator was imitating that usage as much as the Shakespeare-KJV archaic forms to add gravitas to the translation. Oppenheimer is recalling the verse from some edition that maintained the archaic but rhetorically powerful to be present perfect.
The only survival in ordinary speech I can think of is the use of to go as a euphemism for death:
“Oh, Gracie,” Grandma said, “your poor sweet mama is gone forever!” We both bawled and completely missed seeing the funeral home men picking Mama up and heading with her out to their van. Dolores Richardson, The Climbing Tree, 2012.
KarlG's answer covers the phrase that Oppenheimer used; your question also asks about two phrases that he didn't use.
Neither "Now, I become Death" nor "Now, I am becoming Death" has the same meaning. Although the quote begins with the word "Now", Oppenheimer is actually referring to an event in the recent past: the detonation of the world's first nuclear bomb. He "became Death" at the point when that bomb exploded. To say "I become Death" would be a statement about what he habitually does ("On Fridays, I go to the pub and have a drink with my friends; on Saturdays, I become Death, the destroyer of worlds; on Sundays, I play golf and spend time with my family.") and "I am becoming Death" would be a statement about an act that is still in progress ("I am becoming Death, the destroyer of worlds. The transformation will probably be complete by the end of the month.").