Hi Marcy,
If the sites are using your brand name and/or other brand terms, and your brand is copyrighted, you may be able to file a Digital Millennium Copyright Act takedown request with Google: https://www.google.com/webmasters/tools/dmca-notice?pli=1\. As they note in the description on the tool, be very clear about whether the other site's actions actually constitute a violation of your copyright before filing the request.
I think it's unlikely that these new sites are impacting your site's performance in search - I was a little unclear about the JavaScript redirect, though (I'm at work and don't want to click on the links you posted on my work computer). Is it redirecting from their site to your site, or from their site to another site that is the porn/junk site? If it's the latter, that shouldn't be affecting your site at all. If it's the former, you may want to file disavow requests at the domain level for those sites just in case.
If your drop in rankings was caused by these new sites, I would expect to see a drop in performance across the board, rather than for specific queries, so I recommend that you keep digging on other reasons for the drop. I would take a look at the sites that are ranking now for the terms you've lost rankings for. How are they different from your site? What sites are ranking now that weren't ranking when you were on top? It may be that Google has decided that your site doesn't fulfill the search intent for those keywords, so taking a look at the sites that rank now will give you some insight into the kinds of pages that Google wants to rank for these terms. Since these were highly-converting terms for you, consider investing in PPC ads for these terms while you work to regain your organic presence. Good luck!