Differences between それとも ・または・もしくは・あるいは

Question

I've been trying to find out the difference between these four lately but whenever I look up any of them in a Japanese Dictionary, the only thing on the page is the other three options with no explanation.

Is there any way to separate them by nuance? Also, for example, if I was to say: オレンジジュースが欲しいですか。それとも、コーヒーが欲しいですか

...why does it sounds like it is all inclusive? The combination of the particles "と" and "も" kind of makes it sound like you can have both at the same time. Sort of like 両親とも教師です。

Or is it saying "Both at the same time are an option"?

Answer 1

Conveniently, the 類語例解辞典 groups three of these together in one heading and adds the other in a note at the end. Here's what its 使い分け section has to say on the matter:

「または」は、二つのもののうちの一方を捨てて一方だけをとる場合や、どちらでもよいという許容を表わす場合に用いる。

または is used for cases where there are two choices and whatever is not selected will be cast aside, or to show that either choice is acceptable. In these cases, the person making the selection has freedom to make either decision.

「もしくは」は、複数のうち、そのいずれかを選ぶ場合に限って使われる。

もしくは is used in cases where there are several choices, and the options are limited to those presented.

「あるいは」は、二者択一か両方同時に成り立つ場合に用いられるが、どちらでもよいという許容の場合はあまり用いられない。

あるいは is used when choosing between two things and it is possible to choose both of them at the same time. That said, it carries the expectation that there is, in fact, a correct choice to be made or that the chooser doesn't really have freedom to decide between them.

いずれの語も文章語的で、日常会話では接続助詞「か」が、広く用いられる。

All of the above are primarily literary words, and are usually replaced by か in everyday conversation.

それとも(接続)話し言葉的。疑問の内容に限って用いられる。

それとも is used in spoken language. Its use is limited to choosing from what is contained in the question, as can be seen in the following example sentence:

「行く、それとも行かない？」 "Are you going, or aren't you?"