Well, you're not going to like hearing this but:
That's a terrible idea. Whenever search engines see the same post in more than one place, they assume it's been stolen and they downgrade every site where the content is found, not just negating the value of pushing it out to those sites, but actually making things far worse than if you'd never even tried.
That goes only for FULL posts, published on publicly searchable sites, like un-private Facebook profiles, websites, etc.
LinkedIn has an app that can bring in your blog. Facebook has several (I use Networked Blogs). The instructions for each depend on the site and you should get your advice about setting them up on those sites. We really just do WordPress.com here.
As for your website, I'd suggest simply linking to the blog as if it were a different page of your website. If you want, you can purchase the domain mapping upgrade and use http://blog.whatever.com instead of http://whatever.wordpress.com