Ketan,
I'm going to encourage them to publish only fresh content on their real blog, would you agree?
If you look at pretty much any of the blog posts on these forums you will see that more and more everything comes back to content. Original content. Original Content. Did I mention original content? EGOL shared a link with me and I'm sharing it again on another post but it's pertinent.
http://www.thesempost.com/google-rewrites-quality-rating-guide-seos-need-know/
Content used to be king and he wants his thrown back!
Can this actually harm the ranking of their blog and website - should we delete the old entries when migrating the blog?
Duplicate content is something that I am working a lot with right now. There is a difference between duplicate content and plagiarism. What needs to be determined is how the are using this content. Matt Cutts said that roughly 25% of the internet is duplicate content, and a lot of duplicate content is ok, for example if you were writing an analysis, or writing commentary on one of those blog posts then of course there is going to be some duplicate content. That sort of this would be ok.
If they are simply taking the article, and posting it, yet still giving credit, then no its not really doing anything except potentially giving your blog traffic. Take social bookmarking websites for example. Let's look at digg.com. A long time ago digg used to take the entire article and post it to their page and you could actually view everything within their website and everything was all gravy. Now, that doesn't work so well. Now, digg usually writes a little blurb, and provides a link.
Google will look at duplicate content, determine which ever is the best representation of the content, usually who wrote it first, who has the strongest domain etc, and gives the credit to them. The other thing too is that these websites, Havard, NPR, etc have in their favor is that they are prob indexed often enough to guarantee that they are going to get credit first.
As to the question about deleting them. I don't think you necessarily need to delete them, depending on how many articles exist, how much traffic they generate etc. There is a lot to look at. If nobody is looking at them, then sure, you can always do a 301 to one of your new blog posts later down the line. Or maybe your first posts are rewrites or analysis of the articles. Regardless I would provide a link on all of the pages letting people know where you got the information, that way nobody can say you were trying to steal the information.
My thought on this whole thing. If it makes you uncomfortable, it's gonna make Google feel uncomfortable.
Hope that helps! Good luck!
Matt Cutts on Duplicate content: https://www.youtube.com/watch?v=mQZY7EmjbMA&feature=kp
Matt Cutts on Original content: https://www.youtube.com/watch?v=4LsB19wTt0Q