Postdoctoral Fellows are strongly encouraged to apply for independent fellowships and grants. The OUHSC Office of Research Administration emails a weekly summary of all funding opportunities that includes links to postdoctoral fellowships. If you do not receive the email it is also posted on the ORA web site.
In addition, there are institutional training grants in Immunology, Vision, and GeroScience that may have postdoctoral positions. Contact the Principal Investigators for information (for Vision research, Dr. Dan Carr ; for Geriatrics research, Dr. William Sonntag; and for Immunology research Dr. Madeleine Cunningham).
Some fellowship/grant opportunities are posted on the National Postdoctoral Association web site.