Suggestions for a non-traditional interview?
Without more information, I would not assume that they will not ask you about your research, publications, and dissertation.  Assume that they will.  My impression is that they want to go beyond this "CV stuff".

I suggest that you should spend more time to understand the motivations of the organization sponsoring the post-doc and why this is funded as a training grant rather than as something else.  Do they put special emphasis on making their research relevant to the real world (i.e. to policy makers, to the social groups being studied, to the general public)?  Do they aim to develop social scientists that go into non-traditional careers or interdisciplinary work?  What has this organization done in the past that they themselves call "innovative"?  Do they aim to redefine the boundaries and methods of social science?



Regarding how to prepare, there are plenty of books on creativity that have exercises that might stimulate this part of your brain.  But I'd guess that spending time on these books won't provide a good payoff for you.

A better strategy would be to organize a debating group with some peers.  They don't have to be at your university.  You could do it on-line via Skype or Google Hangout.  Arrange a meeting and specify an important+controversial topic in your field.  Focus the debate on how this topic could be researched in a new and different way, such that breakthrough results might be achieved.  For example:


Could the problem be reframed, rescoped, or redefined?
Could new methods be applied or existing methods be combined?
What new methods/approaches have already been tried but have failed? Why?
What methods or approaches from other disciplines might be adapted or applied to this topic?
What if this topic was researched at a much larger scale? much smaller scale? Over a long time period? At a single moment in time but in great detail?
How can research results become more compelling, rigorous, or widely applicable?


And so on.

Basically, your debating group will be exploring the space of possibilities just beyond what is being done today and assessing the prospects of improvement or innovation.

The value of doing this in a group rather than solo is that you will be engaging in the same modes of thinking and communication as the interview. You can and should challenge each other to clearly explain and justify your ideas, and to properly characterize them even if they are sketchy or "wacky".

You might find that this sort of preparation isn't for you.  If so, then maybe you might have to admit to yourself that you aren't an "innovator".  That's fine. There are many other good roles in social science that emphasize other traits and skills.