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Unfortunately, Google may continue to keep those pages in its index for months, even if they return a 404. The 2 best options in these cases is usually: Claim the profile in GWT - which would probably be possible but requires a lot of work with Godaddy configuring the subdomains just so you could claim the profile and de-index. I haven't tried it, but Google introduced a URL removal tools for URLs you don't controll. Might be a good use case here. Here's some info: http://googlewebmastercentral.blogspot.com/2013/12/improving-url-removals-on-third-party.html

Thanks for both of your responses! @IrvCo_Interactive I do have a Webmaster Tools and I do not have any warnings. But I do see 70 errors under Search Appearance > Structured Data, all regarding Missing: author and/or Missing: updated. I will look into what that's about. I am working to fix the weird subdomains coming up in Google for our site. We never used these domains and someone suggested to me that this might be a result of a wildcard A record in my DNS. This other Moz article mentioned to use .htaccess to 301 these, so that might be the fix I use: http://moz.com/blog/find-your-sites-biggest-technical-flaws-in-60-minutes I am not quite sure what I need to do to make sure my site's internal structure is solid, I just set it up in ways that seemed intuitive from a user perspective. I'm sure there are articles out there on this subject though. @Moosa Hemani Indeed that site http://www.hvhtek.com/associates/surfopt/surfopt.html does use a few paragraphs from our site. What tool did you use to identify that this duplication was out there? I have done almost no work on link building and neither has anyone else, so in a sense what we have now is our natural link profile. But our site has been around for a long time so we may have gathered some bad links anyway.