What experiments could provide observable "stringy" effects.
All valid experiments are acceptable (also theoretical experiments).
I will once again state that string theory, any theory, cannot be proven right by any experiment. The experiment might validate the theory, i.e. come as a result of a prediction from the theory.
At the moment there does not exist one string theory in the manner that there exists one General Relativity theory.There are many models based on string theory, though.
Why such an interest? Because at the moment string theories are the only theories that can accommodate the Standard Model of particle physics and at the same time allow for the quantization of gravity, which has been the holy grail of theoriticians the past fifty years. That is they promise a "Theory of Everything, TOE).
What might disprove the usefulness of string theories for a TOE would be if supesymmetry were falsified at the LHC, for example. If nothing is seen other than the Higgs at the LHC, SS would seem as a nice try but bad luck. Then the usefulness of strings becomes doubtful. If SS is seen in the LHC and studied as well as the SM in the International Linear Collider to be built in the future, then strings will be good as candidates of a TOE.
since theoretical "experiments" are included, a proof that any consistent theory of quantum gravity has to be a special case of M-theory will do.