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When one starts out learning Japanese, they're always taught to use the phrase “さようなら” to mean “goodbye.” However, it's now known that it's not that commonly used as people regard it as a kind of “final” goodbye, similar to the phrase Adieu.

And informally, “じゃあ、また” or “またね” are the most common phrases used.

But when one meets a stranger in the streets, for example, how would they say “goodbye” to them?

さようなら would be perfectly appropriate for that situation, since it is likely you will never see them again.

Another possibility is お元気で when you think you won't see someone for some time. It's a little more formal, and it is often used with people you already know and have some kind of relationship with. But I think it could be used with someone you don't know well too, depending on what the nature of the (brief) relationship was.

When one meets a stranger in the streets, how would they say “goodbye” to them?

I can't think of a situation where you'd say goodbye to a total stranger you've just met... and what phrase you'd say when parting with them would depend on what conversation you've just had... for example:

A: すいません、この近くに郵便局はありますか。

B: 郵便局なら、そこをまっすぐ行って、右にあります。

A: ああ、そうですか。ありがとうございます。

B: いえいえ。

A (駅の階段などで): 重そうですね。持ちましょうか。

B: あ、すいません、ありがとうございます。

A: いえいえ。

B: ありがとうございました、助かりました。

A: いえいえ。お気をつけて。

I think the other answers are ok but I just wanted to expand a little to try to give you a different point of view.

when one meets a stranger in the streets, for example, how would they
say “goodbye” to them?

As I said in a comment, this is not very clear. It could depend a lot on how the interaction goes on, what do you say, how old is the stranger compared to you etc.

However, what I want to say is: Don't assume you MUST say "goodbye" just because your native language/culture has taught you that it is the right thing to do.

A very important thing when learning a new language is to "get out" the mentality where you automatically port everything from your own culture.

Just as often "literal translation" does not work, the same is true for cultural habits.

Therefore, to go back to your question, don't think you necessarily have to say "goodbye", whether it is さようなら、では、じゃあ、またね, etc.
Depending on the conversation, it might be perfectly fine to just say nothing.

For example, the stranger asks you for an indication (how to go somewhere or find some place). Then, the conversation might just end with him thanking you, and you saying,　いいえ　or どういたしまして or whatever, and you both walk away. And that's perfectly fine.

If there's a chance of meeting them again, では、また is another option. では is a formal version of じゃあ.