An oaDOI link is like a DOI, with a useful difference: if there's an open access version of the article, the oaDOI URL will send you there, instead of the paywalled article landing page. So for instance,
This DOI links you a paywall page doi.org/10.1038/nature12373,
but this oaDOI link gets you a PDF oadoi.org/10.1038/nature12373
The oaDOI system was inspired by DOAI. It improves on their coverage, and offers an API with license information and other details. It's in active development by the Impactstory team.