Portal Fantasy Question

What works for your story?

With 1 and 2, the issue of communication isn't important, as the story's more about other things - the adventure, or the sense of wonder exploration. Same with 4, to a degree (so long as your world has sufficient magic to allow it.)

With 3, you might create more of a stranger-in-a-strange-land sense of alienation and "otherness," plus you can get some nice characterization, world building, and plot elements in as the MC struggles to learn the language. The struggle can be an integral part of the story.

None of these approaches are inherently wrong, they just fit with different styles and different stories.

Given the overall tone of the post, though, I get the impression you don't like the handwaving or "translation convention," and want to have the MC have to learn the language, but aren't sure if portal fantasy readers want to deal with the language issue. It has been done before, so it's perfectly legitimate and a fine way to write a portal fantasy, and I don't think anyone would stop reading a portal fantasy just because the MC can't immediately communicate with the locals. (If they do, they weren't going to read your story anyway, so don't worry about them and write for the ones who do read it.)

Wow, sounds like these could have greatly varying effects on the rest of your story!

I'm afraid #1 and #2 might bother me (I appreciated when the Magician's Nephew cleared up the use of English in Narnia, for example, but less than that would be annoying. And why does this character come from our world in the first place then? As readers from our world, we're already experiencing the book as a portal (to some degree at least, depending on the immersiveness of your world).
#3 Sounds appealing to me in its authenticity, but also difficult. As in, you will be limiting how well this character can communicate and understand things for a good while (and maybe it works out to skip ahead to the point where they can understand things better, though that seem unlikely).
#4 seems like it depends mainly on the tone of your story, and could easily be annoying or natural. Do you want magic to be an integral part of the world entered through the portal? Are there other kinds of magic that are simliarly used? Do they get explained or have systematic rules?

#1 or #2 would really strain my suspension of disbelief, so I wouldn't use those.

It depends on what you intend for your world, but if the story is going to be very magic heavy, I suggest option# 4.

Option #3 sounds like a lot of work, and not in a way that would be fun to read (though could do a time skip after the initial arrival to get to the part where conversations are possible).

Me personally, I'd go with option #4, but I would not make it instant or automatic. I'd make it so that someone has to craft a magical item or cast a spell for the understanding after the initial linguistic confusion.

If you have an idea for using option #3 and have it somehow be interesting instead of just boringly waiting for the MC to learn how to speak, go for it, if you want.

I think anything from 2 on down could work, but I tend to look at "but magic" as dubious handwaving so clearly ymmv And I generally agree with Brightdreamer. It depends on what you want your book to be. Like, if a big part of the story is how this character gets accustomed to living in this new world, go nuts with 3. If the story is more about action plot beats that happen once they're there, then 2 or 4 are just fine so you don't waste the time of readers looking for that sweet sweet action.

1 and 2 are frustrating and egocentric. I appreciate the realism when different planets, species, or cultures go deeper than a wardrobe change. Babylon 5 was one of the first times I was really happy with how other cultures were represented.

Characters speaking the same language never bothered me personally as a reader. It's sort of part of your suspension of disbelief, especially if character interactions are important.

But if you really want your main character to feel isolated and detached from everything around him, then make it hard for them to communicate.

A lot really depends on the nature and tone of the story you're telling -- are you aiming for gritty detailed realism, or a really magical fantasy? Is the language question even important to the story? If it is, esp if you are trying to do serious world-building and your character is going to spend significant story time dealing with an unfamiliar culture & communication difficulties, #3 is the obvious approach to take. Otherwise, either don't raise the question in-story at all (#1) or dismiss it very quickly (#4) and get on with the story you want to tell. (#2 can potentially work, but you have to be able to hand-wave like a boss to carry it off.)

In a lot of stories I think you can get away with #1 but it depends on how rule-bound your fantasy world is. The more you explain the more everything else should make sense. Drawing attention to it (#2) has to be done in a way that isn't off-putting. There are a few cases where 2 works well (alternate universe stories for example) but I suspect outside those cases it can hurt as often as it helps.

In my WIP novel (which has an infinite multiverse thing going), the main protagonist starts with #4 but she was lucky to land somewhere with friendly people who know about the multiverse and have access to the "magical" tech to enable communication. She meets someone later who had to go through #3 and had a very rough time of it. So those can coexist. If the person falling through the portal is your main point of view character, #4 lets you get up to speed and on with the rest of the story sooner, unless the struggle is the point of the story.

Haha, I'm doing a mix of 3 and 4.

My heroes can't converse at first (but they're not the first from our world, so another character mistakes their English for "Saxon", due to some shared words, and starts speaking to them in Old English,) but then they meet the baddie, and the baddie casts a spell and suddenly they understand each other.

Then the baddie dies, and the spell goes with him, and now the heroes have to learn to communicate with their new friends, right at a time when some serious trauma happens to them, and they need someone to talk to more than anything. Because I'm an arsehole and I want them to suffer.

In the fantasy genre, when someone is somehow teleported into a fantasy world, as in "The Mathematics of Magic", it makes sense that he will be able to speak the local language. (Or he is noticed by the locals and they take him to a wizard who will cast a spell and then the language becomes understandable.)

In SF, when, say, an astronaut crash-lands on an alien planet, it'll be different, of course.

None of them are "least objectionable." Every one can and has been many times made to work.

Another possibility (one that's pretty common in translated Asian web novels) is transmigrating into the body of someone who's just died, or outright possessing them (intentionally or not). The MC is able to sort through their memories and instantly pick up the language, history/culture, and get a place in society.

It's a great plot device because you can throw your MC into the thick of things. What if they've just been dumped into the body of a wanted mass-murderer? Or an heiress who's being schemed against? etc. It also skips a lot of the set-up part of the story ("What's that? What's that?"), which can get old if you read a lot of portal fantasy. IMO quick starts like this are the reason why portal fantasy is a lot more accessible in web fiction as opposed to older fantasy. Okay, that and lots of wish-fulfilment