ORNL does not issue SBIR-STTR solicitations; those are handled by the federal agencies themselves. An excellent source of information on current SBIR/STTR solicitations (and all things SBIR/STTR) is www.zyn.com.
If your company wishes to engage the laboratory with respect to an SBIR or STTR proposal, one way to identify the laboratory's scientific and engineering research capabilities would be to peruse the ORNL Science and Discovery web pages.
For additional information, contact: Mark Reeves, Telephone (865) 576-2577
In the case of STTR, the funding agency will require, from the proposing company that teams with a research institution such as ORNL, evidence that the proposing company has entered into an agreement with the research institution to gain access to any intellectual property developed under the STTR project for commercial exploitation. ORNL provides the following sample templates for an STTR Intellectual Property Rights Agreement for use in such a case.