I agree with Peachey - and in fact his advice doesn't just apply to phrasal verbs, it applies to all words. Next time, try to compare sentences instead of comparing words, and you will get clearer answers. If I asked you, "What's the difference between a monkey, a watermelon and an iPhone?", how would you reply? It's an impossible question, because the differences are so varied you don't know where to begin! The same applies to your question: "take" is such a hugely varied and context-dependent word that nobody can give an adequate answer to your question. Aside from the link Peachey provided, you can try www.linguee.com and www.glosbe.com to find more example sentences.

Take away is to remove something from something. Like in math, to subtract is to take away from the sum of numbers. Take down is to also an action of removing something. Like to take down a picture from a wall or an old poster. It has the action of removing something from an elevated height to a lower one, and to be discarded or put away. Take off is also to remove something. For example, a nurse might ask you to take off your clothing before being examined. Or you are at a sale and using a coupon, but you only want to use that coupon for something specific, you would take off the retail price for the jeans, but not the poster. All of these words indicate removal of something, and the preposition enhances the verb in various contexts. Hope this helped some!

As a start, go to http://yandex.ru/images/ and enter each phrase separately. You will at least see the differences in the physical action of each phrasal verb. If you want to learn phrasal verbs properly, find them in proper sentences. Looking for single definitions for each phrasal verb will only frustrate and confuse you, because we use them very flexibly. The meaning comes from the context.