I don't know how you handle your legitimate urls (your actual articles/pages) with moving from k2 to joomla articles, nor if you had SEF urls enabled/disabled before and now.
It's expected to see your WebMasters console filling up with errors when doing content/url organization changes/restructuring on a website.
However, particularly for these k2/user URLs that's a common issue with K2, where spammers are creating user accounts and then become k2 users with their own user page in K2. This issue pre-existed in your site, but likely you weren't aware of it.
The bigger problem was before starting getting the 404 error notifications (as I guess you started getting now) in GWT, as those pages were actual accessible pages in your site, crawl-able and indexable by Search Engines.
Now with K2 missing, all these URLs result to 404 pages.
A 404 is not necessarily a bad thing. Actually it is what you want to respond to anyone that will try to reach at a page that does not exist.
A 404 error will also tell Google that this page doesn't exist. Eventually these pages will be removed from Google index and this is what you want.
I would recommend against redirecting these "spammy" URLs to real pages. To which page you would redirect them and why you would ever want to do so? If you find out that you have a spammy viagra url/page in your website, you would redirect this to the home page? Redirecting the pages will make google keep those URLs for longer in its index, as it will consider those are real and useful URLs in your site, which all should take visitors to another page.
There is another HTTP response you could return for these pages though:
See here: How to remove Content with 410 Status code
You could implement this like below:
Install again K2 in the new site.
Go and open with a code editor the
just below these lines:
// no direct access
defined('_JEXEC') or die;
JError::raiseError(410, "This page isn't available any more and will never be available again in the future");
save the file.
Try to reach to one of these k2 urls and see what it returns.
It's also possible to do so via .htaccess, but you will also have to create custom error documents to handle the error responses.
If you need the htaccess solutions let me know and I will post later again.