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Canonicalizing http://sub.test.com to http://www.test.com will tell Google that those two individual pages are the same and it should only index http://www.test.com--it won't affect other pages on the subdomain.

If you only have a few subdomain pages that are duplicates of root domain pages, you can just use canonicals to indicate which pages you want indexed. You won't need to noindex the duplicate ones--they will fall out of Google's index naturally once Google sees which are the preferred, canonical ones.

Take a look at the Mozcast for yesterday--108 degrees and stormy!!

Here is a thread about the DMOZ/Open Directory project that ViviCa1 mentioned. [A lot of people are trying to get into DMOZ but can't, you should be happy you have the link. ]

One thing you could look at though is why does Google think that the directory description is the best one to return?

Check and see whether you can improve the descriptive content on the actual site. [At one point I got two new sites to work on, both in DMOZ, the rich, active one returned site-appropriate information, the long-neglected one returned the directory description.]

Our videos hosted on YouTube rank for their YouTube URL, not their URL on our website, when I search by the video title —YouTube is a high authority domain. [And actually they are original content on YouTube—I have to have them there before I can have them on my site, so they have that on their side as well.]

I also have some videos on Wistia (which we pay for) and our website, not Wistia, ranks for those.

URLs that don't exist should display an error page and return a 404 (not found) response.

When you have made-up URLs going to an actual page that returns a 200 (OK) response, the problem actually is that Google will start seeing this as soft 404 errors, which is not good.

From Google Search Console: "Returning a code other than 404 or 410 for a non-existent page (or redirecting users to another page, such as the homepage, instead of returning a 404) can be problematic. Firstly, it tells search engines that there’s a real page at that URL. As a result, that URL may be crawled and its content indexed. Because of the time Googlebot spends on non-existent pages, your unique URLs may not be discovered as quickly or visited as frequently and your site’s crawl coverage may be impacted..."

You'd be doing this with the big site's permission, right?

Then yes, as Chris said use a canonical pointing to the original source. That content on your site won't be indexed, but it will be there for visitors to your site to read without leaving your site, which is why I am assuming you'd do this in the first place.

And to make a quick point about the dreaded "duplicate content penalty"--it's not a penalty as such--Google just makes a call on which version to index and which one to drop. In this case, the original would probably indexed with or without the canonical (though you should use it anyway).

That being said, if you have a lot of scraped content, Google may not consider yours to be a quality site and that creates problems.

Was any type of work done on the site the day of the spike?

I concentrate on the "most normal or typical sites will not need to use this tool" part, myself. (Though it sounds like you may not fall into that category.)

So then it's back to downloading as comprehensive a list of links as you can by using various sources and looking them over. (Also, in the past I have used LinkResearchTools to get an overview--it isn't cheap but it is a lot less than $140,000.)

Post transcripts--it costs about a dollar a minute for a service. If you can't afford to do them all, do the most important ones and post summaries for the others.

Can you have newengland.theaterclub.com redirect to boston.theaterclub.com? Or at least no one else is going to use newengland.theaterclub?

Those urls are long enough that no one is likely to be just typing them in, so that's probably not your biggest hurdle. And most people searching for theater tickets in New England will be looking more specifically [I live in New England] and Boston is likely your biggest target anyway.

So, ideally your url should match your other naming, but in this context I wouldn't make changing it your first priority. [I mean the Foxborough Patriots are managing to get by using a more general name...]

If people are enjoying your posts, they may well want to have a trial signup. This is a very common practice and a lot of the reason people have blogs to begin with.

First, are you sure you need a link audit? Google is pretty good at ignoring regular spammy links that get picked up over time by large sites, as they say in their "Disavow backlinks" help page.

If you think there is a cause for concern, Moz's own Open Site Explorer can give you a list of incoming links that includes a spam score for those links, which can be used as a first pass.

The general drill for a manual link audit is to find all of the links you can (search console, moz, ahrefs, majestic, etc.) and create a de-duped list. From there, the "definitely good links" are usually easy to spot--you will recognize them from your industry or from other authoritative sources. And you will probably recognize the spammy "Get Rich/Viagra" backlinks as well. (If you sort your list by domain, it is easier to pick them out as a group.)

The rest are the ones to look at more closely.

But as I said to start, unless you think you are being penalized, tread lightly when it comes to disavowals.

To quote from Google [about disavowal]:

"This is an advanced feature and should only be used with caution. If used incorrectly, this feature can potentially harm your site’s performance in Google’s search results. We recommend that you disavow backlinks only if you believe you have a considerable number of spammy, artificial, or low-quality links pointing to your site, and if you are confident that the links are causing issues for you. In most cases, Google can assess which links to trust without additional guidance, so most normal or typical sites will not need to use this tool."

The other question is how will the "link bait" page be found by potential linkers? It won't show up in search anymore, if you point a canonical to the other page. [Maybe it is just very easy to find from another popular page on your site, which is easily findable?]

Are the new pages you are adding in Google's index? Since you are an ecommerce marketplace maybe Google is dropping old products as it is adding new ones.

Could a robots disallow have been mistakenly added to some pages, blocking Google? Or a noindex meta tag? (If you know of a specific page you'd expect to be indexed that isn't, you can check those.)

Under crawl stats, you can see how many pages are crawled each day. Has that changed? If so, did anything change on your back end the day it changed?

If you go to the OSE results page, start clicking on the links, view source, then do a search for APBSpeakers you will find them. Here is the Huffington Post one, for example: “When I turned 5, I had had symptoms of AIDS. I had had fungus in my brain, blood infections, pneumonia,” Hydeia told Oprah back then.

rbkyf

The cnn link is on this page: http://www.cnn.com/2015/02/26/opinion/david-love-medgar-evers-trayvon-martin-survivors/index.htm

In this paragraph: Meanwhile, not unlike Myrlie Evers-Williams, Sybrina Fulton found her calling through grief nearly 50 years later.

I took a quick look at those links and I am not sure why you think they are black hat. They seem to have a lot of well-known clients which would account for the authoritative domains.

And when I clicked on the sites listed in Moz, I saw that there were in fact links back to APBSpeakers.com. [Even if the company wasn't named, its speakers were--you have to look at the page source, not just do a site search.]

Why do you have it set up that way to begin with? Could you put the content on the higher level page? Or is it meant to be an easy-to-remember "vanity" URL? In any case, yes, do not put a page with no content in your sitemap.

And to get it to stop showing up in search, you can add a canonical to the page, pointing to the deeper page with the actual content.

Moz's rankings can change from month to month depending on the current index--you shouldn't rely on them as an absolute value. Have your competitors' ranking also dropped? Here is some info from Rand about fluctuations.

It could have to do with the other issue you wrote about, hijacked content. If that other site is taking your content, Google may be seeing it as a duplicate content situation and deciding (for whatever reason) that the other site is in fact the one that should rank. This would result in your site disappearing from the serps for that content. [Assuming that you see this other site appear when your pages disappear.]