Either he or I am going.

Answer: Option A

The correct answer is Option C: I or he is going.
Here's why:
The original sentence, "Either he or I am going," is grammatically incorrect.
When using "either...or" with different subjects, the verb should agree with the subject closest to it.
In the original sentence, "I" is closest to "am," but "he" is also a subject and it creates a confusion.
Option A: he or I are going is incorrect because "are" doesn't agree with "he".
Option B: he is going or I am is grammatically correct but not improving the sentence; it changes the meaning and sounds awkward with the inclusion of the word "either".
Option C: I or he is going is the best option because it uses "is" which agrees with "he," which is the subject nearest to the verb, and maintains a natural flow of English.
Also, putting "I" first sounds more natural.
Therefore, "I or he is going" is the improved and grammatically correct sentence.