Does copyright restrict how I can adapt papers when compiling them into a thesis? I am starting to put together my PhD thesis. The bulk of the thesis will be reprints of papers I have published during my PhD. I am wondering about presentation style. 

My personal preference would be to reformat all of my papers into a single LaTeX document so as to have consistent style throughout. It's a bit of extra work, but I would prefer this approach. In several cases my papers have supplementary info which would not fit in the constraints of the main manuscript in the published version, but which could (and probably should) be coherently woven into the main text. 

Are these acceptable options? Assuming I get reprint permission from the publishers, is it acceptable to change or partially reorganize the text for the sake of a coherent narrative within the context of the larger thesis? Or do copyright laws require that my reprints be exact reproductions of both content and style as compared to published versions?
I disagree with part of the other answer, in that the copyright holder of a work is not always the creators/authors. For some journals when you publish with them and sign the licensing agreement, you transfer the copyright of your work to the publisher. Then it is up to the publisher to decide how you can reuse your paper. I would advice reviewing the copyright/licensing agreement you signed with your publisher for limitations for reuse, and if still in doubt, contact the publisher.