This may sound very weird but I like the style and layout of stackoverflow's menu at the top, with a search centered and other menus to the right side. Is there a way to apply this to the rest of the stackExchange or at least this stack?
It sounds like you're asking about the top bar, where the inbox, achievements, and links like "review" and "help" are. Stack Overflow changed that all around; it doesn't look like the other sites on the network. That's not part of a site's design; that's baked into the SE code, currently only on SO and its meta. I believe they intend to roll out something like that across the network at some point in the future, but I suspect it'll be a while. (Some of the links on SO are only on SO, like Documentation and Careers, so they'll at least need to change that. But I think they'll probably use SO's users to work out bugs and analyze how people are using it differently before they broaden it.)
Whilst we are still in beta for this stack exchange we are unable to change our layout.
But rest assured as soon as we get out of beta we will all pitch together to make a layout fitting for the site