Does publishing in journals known as "predatory" hurt one's reputation? Does publishing in what is known as a "predatory" (such as OMICS) journal diminish ones reputation? Do these publications help at all when applying for grants (or do they impede ones chance)?
Yes, your reputation is diminished, because people will think you couldn't get published any other way.  It will actively harm your chances at pretty much any interaction with reputable organizations, including grant proposals.  Don't do it.