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Page 16 and Page 17 are not necessarily duplicates of each other but since each page is showing the entirety of the articles, instead of a snippet/preview/etc, every article would be a duplicate of the exact content showing on those pages.

So, I'd definitely agree with NoIndex on those pages.

Choose what works best for the product and fits naturally into the content. You need to remember that the search engines will decide what they think you're most relevant for and rank you accordingly.... which means that just because you optimize for "Cowboy Chinks" doesn't mean you won't also rank in the SERPs for "chinks" and "western chinks". Google recognizes synonyms in content. Write for people, not for the bots... unique, informative content that will best serve your customers is better than attempting to force in every keyword imaginable in the hopes of ranking for everything with a single page. And once you start writing it you just might realize you could fit all or most of those naturally into your content.

Based on my limited experience of this type of situation, I've felt a good start is to Canonical each page on the old domain to its counterpart on the new domain and place a call to action on the old sites letting people know of the move and/or branding change. Submit for crawl request, let the bots begin filtering through the changes without affecting user experience yet. Then after some time, so your regulars have become acclimated to the upcoming changes and so have the bots, you can 301 those pages from the old site to the relevant counterpart they were already canonicalized to.

After reading the further responses here I'm wondering something...

You switched to a new site, can't 301 the old pages, and have no control over the old domain... So why are you worried about pages 404ing on an unused site you don't control anymore?

Maybe I'm missing something here or not reading it right. Who does control the old domain then? Is the old domain just completely gone? Because if so, why would it matter that Google is crawling non-existent pages on a dead site and returning 404s and 500s? Why would that necessarily affect the new site?

Or is it the same site but you switched to Java from PHP? If so, wouldn't your CMS have a way of redirecting the old pages that are technically still part of your site to the newer relevant pages on the site?

I feel like I'm missing pertinent info that might make this easier to digest and offer up help.

From what I understand, when combining open graph protocol and meta description it needs to look like name="description" property="og:description" content="My meta description copy."/>

DO NOT just blindly Disavow Links. The tool is really only intended for use when you have received an Unnatural Links warning or you have a massively spammy link profile that you're preemptively taking care of. Disavowing Links improperly can wind up hurting you.

If another site is linking to pages on your site that don't exist then the correct course of action is the 404. You could always try contacting them to tell them about the broken links pointing to your site and ask if they can be fixed or removed them as needed. Ultimately the 404s on your site are not harming you and they are also not benefiting you via any link equity because your page does not exist so there is nothing to pass the equity on to.

If you actually receive a decent level of traffic via those links or if a large number of valuable links are pointing to the 404'd pages, THEN you may want to consider redirecting somewhere else. If the other site is a spammy mess or you have 1000s of crap links pointing to you, then I'd say you might need to do a Disavow. But currently it would seem to me that you could let the pages 404 and get on with your day.

A plugin like Yoast will give you the ability to set your archives to NoIndex, Follow which should alleviate your issues.

Personally, I wouldn't worry about redirecting a handful of pages that have been 404ing for 6-7 years. Odds are they don't rank for anything, Google has removed them from the index and they'll have little to no traffic going to them. Though I don't think they'll hurt you if you were to redirect them to a relevant live page... I just don't think you'll gain much from doing so.

Not that I know of... but even if they did it would only be an approximation of what they could gather were search volumes based off of trends. Whereas going through something like Adwords would give you the data straight from the source (more or less). There are also other tools out there to help with that data as well such as Wordtracker (like BeardoCo mentioned) and SEMrush which offers some organic keyword volumes along with the rest of its data.

That's a tough one without more information. So I'll go into part of my standard WordPress spiel...

Other than categories, what are you doing about Tag Archives and Author Archives duplicating your content? Are you using tags properly or do you have tons of one-off tags everywhere? Do you have your homepage & archives set to show the full article or only a preview? Because if everything is set to full article, you're tagging like crazy, and your archives are all being indexed... every new post is being duplicated a minimum [4 + (# of Tags)] times on your site.

What are you using to try to handle your duplicate issues? Practically everyone suggests using Yoast.

Yeah... if you're using the Wordpress platform hosted through Wordpress instead of through an independent hosting solution then you can't add plugins so you're a bit stuck on that as far as my knowledge goes.

That odd URL is the link in the image on the right side of your site for "lose weight today with gastric band hypnotherapy".

I used Open Site Explorer to find what pages were linking in and they all mention "(img alt) gastric" which made it easier to pinpoint where on the pages the link was coming from.

Take a look at the Moz Help Page Why Isn’t My Site Being Crawled? You're Not Crawling All My Pages!

It lists the most common reasons for your issue.

Having pages that no one goes to won't negatively affect the rankings of the rest of your site.

In your case if you're really concerned about those obscure pages and they're thin or duplicate content, you could choose one really popular product in each category (such as "6x6x4 red foil gift box") and add canonical tags on the other similar products in that category (i.e. all the other red box pages) pointing to the popular one.

It may not be in Moz Analytics yet but it will be. When I first switched, only 4 of my 5 campaigns appeared. So i kept having to switch back to Pro to access the fifth one. Eventually it too got updated in Moz Analytics.

You definitely do not want to NoFollow your internal links like that. Link Equity will still be divided by the number of links on the page but all the NoFollowed links will suffer because they won't pass equity anymore. I agree with Angelos' idea. Split things up into category pages where possible so you can move some of the links off of the nav bar and into a page which will better serve visitors and give you another place to include unique & relevant content that could help your site rank.

This is not an uncommon problem. Take a look at this Moz Help page for the most common answers to your problem: Why Isn't My Site Being Crawled? You're Not Crawling All My Pages!

I think what may be happening is that you said you're looking in Google Analytics for it but the steps say to check Google Webmaster Tools.

That is yet another reason Rel=canonical was created... for when one page is a subset of another page. E.g. Your Nike page is a subset of the Trainers page.

I suppose the most important question is What will be replacing them?

You don't necessarily want 30k 404 pages appearing overnight like that and causing issues for visitors. Personally I'd say you should go through all the pages to determine what the most relevant alternative page is and then 301 redirect the old pages to the new ones. That'll be a lot of work for 30,000 pages but it would probably be the best way to save from inadvertently losing traffic, backlinks and positive link equity.