Is there a Post-doctorate Equivalent for an ABD (All-But-Dissertation) status? I am an ABD (all- But-Dissertation) student. I have done all my work, completed my credits, passed my qualifying exams, I passed my oral exams, but I am having trouble finishing my thesis (advisor problems) , and
I was wondering if there may be some variant of the standard post-doctorate for
people in an ABD status. 

EDIT: Basically,  are there post-doc programs that will accept someone who did all the work but did not finish their thesis? Or are there programs similar to a post-doc for people who have

SECOND EDIT: I am in a Mathematics Program. Does anyone know of schools that will
allow me to transfer with relatively few requirements, i.e., not needing to take years worth of classes?

Thanks.
The fundamental misconception is that there can be "someone who did all the work but did not finish their thesis".  The thesis is the focus of a Ph.D. program, while coursework and other requirements are nothing but preparation for the thesis and are of negligible importance in comparison.  Postdoctoral positions are meant to give people a chance to deepen their research experience beyond what they achieved while writing a thesis.  If they haven't written a thesis, then they haven't completed graduate school and do not yet need to move beyond it.

Occasionally people do begin a postdoctoral position without yet having received a Ph.D.  This happens when they have completed their doctoral research but have not yet graduated, for example because their institution awards degrees at only a couple of times each year.  I've never heard of someone starting a postdoc if their thesis wasn't at least nearing completion, and I think it's so unlikely that it's not even worth looking into (although I can't conclusively rule it out).

Although postdocs per se are not the right program for this, one could reasonably ask whether there is anything else.  There are plenty of postdocs intended to help recent Ph.D. graduates gain additional experience, but are there any programs aimed at helping students who are struggling to finish their degrees (perhaps for reasons beyond their control) become successful and productive researchers?

Unfortunately, I don't know of any.  The general feeling is that this is the responsibility of the department you are studying in.  They know better than anyone else what you have accomplished so far and what your future potential is.  If they have faith in you, then they can help you try to find additional funding, transition to another advisor, or whatever might be appropriate.  If they don't have faith in you, then it will be difficult to convince outsiders to take up your case.  It could happen in theory (if, say, a faculty member somewhere else is impressed with you and helps you transfer), but I don't think it's likely.  Looking outside your current department/university will be seen as a sign that they have given up on you, and unfortunately that will tend to put other institutions off.