The Bechtel International Center website has detailed information about visas and other topics for international scholars and visitors. It's really well done; there's a lot of very useful information, examples of letters and you can down load forms etc., and you can find it all on their website. See especially the pages focused on international scholars for resources of interest to postdoctoral scholars.
 
If you are currently a post-doc and in a process of becoming a lucky Research Associate, Shirley Harris from the Bechtel centre said that she has heard that, if you are being appointed as a Research Associate, it is necessary to have at least 6 months remaining on your J-1 visa if you wish to keep your J-1 --at least until another visa can be secured.
 
Find out if you are subject to the 2 year home rule!!! This rule means that you have to return to your home country for two years before you can get another US visa. Check your visa stamp in your passport (where your picture is!). It is indicated at the bottom of the page if you are subject to the `212e' rule (which is the 2 year home rule).
 
Administrative office hours are:
 
10 a.m. to 5 p.m. Monday through Friday
 
The Bectel Internation Center website maintain a list of immigration attorneys that you can access should you need one.