The "one stop shop" for information is the Association of State and Provincial Psychology Boards (ASPPB,
www.asppb.org). They publish a directory which summarizes each jurisdiction's requirements (and provides links to the pertinent web sites).
Also Ken Pope's web page (
http://kspope.com/licensing/index.php) has links to the licensings boards.
When I checked during graduate school (2000 - 06) only 10 states required graduation from an APA accredited program for licensure.
No state required an APA-accredited internship.
That said, most states accept graduation from an APA accredited program as de facto evidence of meeting their state standards, so it is much easier to navigate the process. But easier does not mean necessary!
[However, it is becoming more common for post-doc fellowships and some employers to require graduation from an APA program
and completion of an APA internship.]
With rare exception, informal post-docs are generally acceptable. In the final year of supervised practice, most boards are more interested in insuring you had someone "looking over your shoulder" for that year, instead of the more structured experience of internship. However, the requirements for what constitutes "supervised practice" can vary wildly from state to state. In general, though, the biggest variable usually is number of hours.
Informal post doc does not automatically mean unpaid. Usually it means accepting a job. Given that formal post-docs pay less (they are providing continued education and ususally expanded supervision), many post-docs prefer to strike out professionally. Of course, there is the conundrum: 1) there just aren't that many formal post-doc fellowships; and 2) since you are not licensed, you are not reimbursable by insurance which means for most jobs, you are a liability not an asset. So most jobs are with state agencies which, ironically, can ignore state licensing requirements.
When people say "informal" post-doc what they usually mean is that they have made arrangements to work under the supervision of a private practitioner. For most jurisdictions, this is perfectly acceptable. However -- many jurisdictions are quite clear that the supervisor cannot be paid for providing supervision of a post-doc. And, as mentioned before, as a post-doc you have no license and cannot bill insurance. So the practice has to either have a solid clientele of self-pay patients or you have to come with a Master's level practitioner license.
Before you graduate, you
must take the time to review the requirements of any state you may
potentially seek to be licensed. Some of the educational requirements must be included
ON your doctoral transcripts. The circumstances aren't quite as draconian for post-docs. But still, before you embark on your post-doc year, you should confirm with the licensing board of any state you may
ever want to license in, if your post-doc will be sufficient.
[Oh and people can and do take unpaid post-docs -- and internships too. The cold reality is that every license-eligible graduate program requires an internship before you can graduate. And 49 states require a post-doc before you can license. [Sole exception: Washington] Given the lopsided supply/demand between applicants and internships -- which is even more pronounced when you get to formal post-docs -- some students feel they have no choice but to accept an unpaid internship/post-doc if they ever want to end their pre-license years.]