Are GREs required for US postdocs? Do universities in the United States require GREs for postdocs in engineering?
Typically, GREs are required for entry to graduate school, not for being hired as a postdoc.  GRE requirements are set by admissions committees who are collectively filtering a vast number of applicants with little background records.  Postdoc hiring, on the other hand, is typically handled more as an individual professor hiring an individual employee.  A particular professor might ask for GRE scores, but to the best of my knowledge that would be quite unusual, as they would typically be more interested in your thesis, publications, and other such recent and directly relevant scientific accomplishments.