Is there a way to post an archive of my past emails sent through VerticalResponse on my website?

Yes there is! After you sign into your VerticalResponse account, go to the dashboard for the Sent Email you would like to share and click the "Share Email" link in the left column (as in the screen shot below); copy the URL in the popup window and you can use that anywhere that you would use a URL link, an email, a website, another newsletter, a blog post, a twitter tweet, facebook, etc.

To share a sent email from your VR account on twitter or facebook, you'll need to link your VR account to your twitter and/or facebook account. The instructions for doing that are covered in this tutorial: Share Your Email on Facebook or Twitter.