First make sure what you're dealing with.
- Go into Google Analytics >> Acquisition >> Organic and find the week (or day, if you can) of the drop in organic traffic.
If you don't have GA, you can try something like Searchmetrics.
- Correlate to this:
https://moz.com/google-algorithm-change
- Look for recovery in organic traffic.
If you think Penguin is still impacting you, I'd recommend requesting removal. In my experience it's not very effective to seek the removal of links, but it's worth a try. If you don't think it's impacting you or still affecting you, just do good stuff going forward. In either case, submit a disavow on the bad links. Don't get caught up fixing things that aren't impacting your site.
If there is an organic impact, this is what I'd suggest.
-Start with a good form letter. Include the URL where the link is located, write up a professional, well-phrased request, and send it out. If there are a ton of sites, you might want to have someone who knows a good link from a bad link sort it for you and gather contact info.
-Send a follow-up to sites that don't respond.
-Submit the disavow and wait for an update.
You could hire someone to do link removal, but I don't think it's often a good way to spend money. Many of these sites are abandoned, and no one is reading the email.
If it's Panda after all, submit a new question and we'll talk 