A mechanical earth ground to the metal of the strain gage itself. It is acting like an antenna. Not knowing what your local sources of RF noise are, it would be hard to say what might be inducing the noise. You could also try running the wires through some ferrite beads as well as twisting the wires from each strain guage. All are ways of reducing the level of interference. Shielding around the wires from the strain gages. Ground shield wires AT ONE END ONLY. Preferably the end closest to the amp.