They are all grammatical. Merriam-Webster gives three definitions of graduate in connection with schools.
1 a : to grant an academic degree or diploma to
1 b : to be graduated from
1 : to receive an academic degree or diploma
If you are talking about a single student, the intransitive verb—"He will graduate in May" or "He is going to graduate in May"—is what is generally used.
Your second sentence: "He will be graduated in May," is the passive of *"X University will graduate him in May," using definition 1a (transitive). This sentence sounds strange to me because people usually use the intransitive in the active voice rather than the transitive in the passive voice (unless they have a good reason to use the transitive). However, "X University will be graduating 5,000 students in May" sounds perfectly fine. And you can come up with situations where the transitive in passive voice sounds fine with a single student, for example, "We will not be graduating Bob this year, but Ray will be graduated in May."
Definition 1b (transitive) appears in constructions like "I graduated MIT in 2009." This construction sounds informal to me, possibly because it become popular only after I learned English. I don't see any reason not to use "from MIT".
Google Ngrams shows that the transitive (1a) in passive voice was commonly formerly used for this, but is now rare, and that the popularity of (1b) is growing. However, the intransitive is generally what is currently used.
I am not going to go into the difference between going to and will in this answer; this difference has been hashed out several times on EL&U. For this sentence, both constructions are fine. The likelihood of graduation is the same for both constructions, and I consider them both acceptable in formal letters.