Certain string theory predictions can be tested in planned gravitational wave experiments like LISA. Also next generation CMB observations (Planck satellite) may also be able to check some string theory predictions.
I am not a string theorist, though I have read quite a few string theory papers. I wouldn't say all aspects can be expected to be experimentally tested in the next few years but I know some people are planning the above mentioned tests.
By the way, a friend of mine is a leading string theorist and he is not a big fan of Greene's to say the least.
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