Which do you prefer, the oceans or mountains?

In this type of sentence, you wouldn't normally say "the oceans", instead you would say "the ocean". You could also say "the beach".

You could also put "Which do you prefer, oceans or mountains?". This type of sentence you can do it many different ways and it still makes sense and can work.

My home town is popular asfor being a beach town in Japan, and I can be relax when I'm exposed to the sea breezes.

You could also say "I can be relaxed when I'm exposed to the sea breeze", or "and I am relaxed when exposed to the sea breeze".

But I've been so scared of swimming in the sea since I saw "JAWS"Jaws.

For clarification it is okay to use (" ") or italics for the film title Jaws if writing formally such as in a review.

Which do you prefer, the oceans or the mountains?

The other correction is right too, but it's also not uncommon to use "the" before both in "this or that?" questions like these.

My home town is popular as a beach town in Japan, and I can beam relaxed when I'm exposed to feel the sea breezes.

"exposed to" makes sense grammatically, but it sounds unnatural.

But I've been so scared of swimming in the sea since I saw "JAWS"Jaws.

Technically, the correct way of writing movie and book titles in English includes italicizing it (setting the font to italics). No one does this in casual writing, but it's still important to capitalize the first letter of the title no matter what.

Which do you prefer, the oceans or mountains?

I definitely prefer the beach.

My home town is popular as a beach town in Japan, and I can be relax when I'm exposed to/ near sea breezes.

But I've been so scared of swimming in the sea, since I saw "JAWS"Jaws.