I would recommend getting a book about particles... even something like A Dictionary of Japanese Particles. Which is only about $15 (USD) at present.
Something to consider before getting into the particle combinations is the idea of は and が. There are a lot of different rules (sometimes seemingly-contradictory rules,) for は and が. But for the sake of simplicity, just remember that は is often the first, main subject of a sentence. が is kind of the second main subject (the "newer subject" or "focus point",) of a sentence.
Now let's get into the combinations from the question.
According to A Dictionary of Japanese Particles:
- とは is a combination of particles と and は
- can mean: "the thing/concept/idea called" (i.e. ボタンとはなんですか。）
- can mean: with (i.e. わたし、Aさんとはスポーツをしたり、勉強したりします。）
- can mean: "surprise/shock about something" (i.e. あの人がそんなバカなことを言ったとは・・・）
In the first example, とは actually seems related to when って is used after dialog, like this: 「ボタン」って、何ですか。 ("Button" <- pointing to subject, what is?) It's a sort of marker for the previous word... something that makes a sort of subject out of the phrase before とは.
- When のは is used, it often refers to a subject (placed in front of のは,) for example:
- 勉強をするのは難しいことです。(i.e. Studying is hard. -or- The thing of studying is hard.) Using のは like this effectively turns a subject (a noun or a concept,) into a subject of the sentence.
- のが is similar to のは. But the difference comes down to the difference between は and が (explained earlier.)
- So if we go back to the example used for のは and replace のは with のが:
- 私は勉強をするのが難しいことです。(i.e. For me, studying is hard. -or- For me, the thing of studying is hard.) Here, the main subject of the sentence is "私 myself". But when のが is used like this, のが (like のは）still effectively turns a subject (a noun or a concept,) into a subject of the sentence, but here, のが is pointing to a "new subject" of the sentence (the thing of studying.)
- With the example given with のが, ことが is essentially the same thing. It creates a concept from a given noun, verb, or phrase.