I don't think "órgano de expresión" can be taken in isolation as meaning a body in which people express themselves; I think it is related to what follows: "de expresión" and "de formulación de leyes" are both qualified by "de las comunidades autónomas", so this means "un órgano de expresión de las comunidades autónomas": a body that gives expression to the autonomous communities, and also drafts laws for them.

I would be inclined to express this as "providing a voice for". My first thought was "mouthpiece", and I think that could work, but it's a word that's often regarded as pejorative or derogatory, so perhaps it might be safer to avoid it.

So it could run something like: "the Senate is supposed to provide a voice and formulate laws for the autonomous communities", or "a body that provides a voice and formulates laws", to stay a bit closer to the original.

"Providing a voice for" is a fairly common expression in this sort of context, I think: a forum that enables people to get their views heard. Here's one example:

"Vela Launches Group To Provide A Voice For Residents With Disabilities"
http://www.velagroup.co.uk/main.cfm?Type=NI&objectid=2662

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Note added at 48 mins (2012-07-22 12:01:48 GMT)
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Or you may prefer to rearrange it like this:
"provide a voice for the autonomous communities and formulate/draft laws for them".

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Note added at 1 hr (2012-07-22 12:24:47 GMT)
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The basis of this is the constitutional definition of the Senate:

"El Senado es la Cámara de representación territorial" (CE, art. 69.1).

Many people feel that in practice it does not fulfil this aim, and there are proposals to reform the Senate to make it more responsive to the autonomous communities. So I think the idea of the Senate as a body in which the regions can make their voices heard is the real point.