I'm not sure there are highly-focused, dedicated efforts under way to find experimental/observational evidence that will directly contradict SST (SMT?). Rather, there is a wide range of astronomical and astrophysical research whose results may play a significant role in falsifying (or supporting) SST.
AFAIK, SST/SMT has yet to make clear-cut predictions which can be directly tested, e.g. the mass of the Higgs, or the that of the LSSP. Of course, there are SST post-dictions, but they don't really count.
The Stecker paper which we've discussed elsewhere in PF gives some indication of what may be discovered in the high-energy regime (cosmic rays, ultra-high energy gammas). Other areas of active research which may be good tests of SST include:
- on-going cosmology research (WMAP, distant galaxy - and cluster - distributions and compositions, expansion rate of the universe at high z, ...)
- the ESSENCE project ("Equation of State: SupErNovae trace Cosmic Expansion" aka "the w project")
- searches for local dark matter, e.g. that associated with the growing list of small galaxies being cannibalised by the Milky Way
- gravitational waves (LIGO, VIRGO, ...)
- neutrino telescopes (esp AMANDA II)
- the next generation of space-based gamma-ray observatories (SWIFT, GLAST, ...)
Perhaps most exciting will be the serendipitous discoveries [:)]