I'll give you a British perspective. Basically, these words all have the same meaning. 'Rubbish' is British English, while both 'trash' and 'garbage' are American English. But it isn't quite that simple. Everyone in Britain understands all three words, and many of us use all of them from time to time. When speaking literally, of the stuff we throw out and is collected regularly from outside our houses, we generally say 'rubbish'. But there are occasions when 'trash' is used - it's common to describe poorly written novels as 'trashy', for example. And if someone writes something that is complete nonsense, we could call it 'total garbage'. The more words we have available, the more expressive we can be. It would be interesting to hear a US English speaker's view on this.

In American English, "trash" and "garbage" are pretty much synonyms. However, "garbage" refers pretty much exclusively to the refuse you put in a trash can, while "trash" can be used both literally and as a descriptor of something that isn't tasteful (usually in adjective form: "trashy"). Rubbish is almost never used.

They are all synonyms with approximately the same connotation. I'd feel free to use them interchangably, but "rubbish" sounds old-fashioned.

Being in England, I use the words in the same way as Su Ki. "rubbish" and "trash" are good verbs too. e.g. "He rubbished his rivals achievements" = he talked in such a way so as to diminish the value of the achievements. e.g. "The media trashed his reputation when they published details of his alcohol problems" This is worse than just "rubbishing" someone's achievements - his reputation is destroyed. When there is a wild party, the house might get "trashed" i.e. the decor and furnishings are badly damaged.

I think all of these are synonyms. However, trash&garbage are commonly used in the American English whereas garbage is popular in the British English. It doesn't have to be truth though. I'm not any expert indeed, that's only my opinion:)