Thank you Kristina,
I know about the URL structure, I have been trying the past few months to cleanse this site that I was not involved in its creation. It has several more SEO problems that have either been fixed or not yet, but we are talking about more than 50 SEO problems I've found so far - most of these critical.
On the sitemap that I built, the junk pages do not exist, and because this is sitemap I have written myself, I can easily make another containing the articles that I have removed (just reverse a part of my select query for the sitemap to get the ones I have removed).
http://www.neakriti.gr/webservices/sitemap-index.aspx
So far I implemented the last of your suggestions and here is an example:
This is a valid article page
http://www.neakriti.gr/?page=newsdetail&DocID=1314221 - (Status Code: 200)
This is a non existent article page (never existed at the first place) - (Status Code: 404)
http://www.neakriti.gr/?page=newsdetail&DocID=12345678
This is one of the articles that I removed from sitemap and site - (Status Code: 410)
http://www.neakriti.gr/?page=newsdetail&DocID=894052
Also I would like you to take a look at another question about the same site and see that it can relate to this question with garbage articles too...
https://moz.com/community/q/multiple-instances-of-the-same-article
Thank you so much!