Can I say "He encountered WW2"?

That would sound rather strange to me as a native speaker. Could you describe more what you're trying to say by that?

Need some more context but that's an unusual construction

faced, probably

It’s an odd thing to say? It might be used for humor or in certain unusual circumstances. It’s definitely “marked”.

That's unlikely to be a natural construction, but there are some situations where it might make sense. Maybe if somebody was reading history and was completely unfamiliar with the idea of World War II? "He first encountered WW2 in his grandfather's old encyclopedias."

probably not, unless you're being dry/ whimsical.    James Thurber: "suddenly, world war two happened to Harold Ross. god, how he pitied him!"   you don't just come around a corner and encounter a war.   encounters are usually unexpected, and they're also usually pretty specific and finite in scope and duration.  

I would probably say that he lived through World War II.

Weird construction. I could see it arising naturally ("during his research, he encountered WW2 repeatedly"), but even there, the phrasing is slightly off. What are you trying to say?

In general no. That would be like saying "He just happened to find WW2" in some very specific and odd contexts it could make sense. But I get the impression you're trying to say that he experienced WW2. If that's the case we'd usually say something like "He lived through WW2".

Sounds a little off you can say: He was in WW2 He fought in WW2 He survived WW2

If he was a time traveler, then yes some situations work.

I don't think so