Considering this sentence:
Something was awry but neither Alice nor Bob knew what.
Can I omit the neither here?
Something was awry but Alice nor Bob knew what.
It sounds reasonable, but I found it strange that it requires a list to make this negation work. When it's just Alice, more words are required to express negation:
Something was awry but Alice did not know what.
The neither is required.
Neither ... nor acts as a negation which as you correctly note would otherwise require "did not" (past tense negation in English is a bit verbose).
You could also have written
Something was awry but Alice and Bob did not know what.
(Note that the "neither...nor" turns into "and" here, one of those rare instances of linguistic grammar conforming to Boolean logic).
