What do you want to remove… your site or the illegal links?
It is hard to say how to remove the links to illegal stuff without knowing how your adding them. I would assume that it is a third party script and that third party not only hosts but provides the products to be downloaded. If that’s the case, you will have to see if that script (or API, if that’s what they have) allows for content filtering. If they do, then you will have to figure out if there’s a common term that you can use to search for those and remove the links (or products, if that’s the case).
The only people that can know this is the third party that provides you with the links.
If you simply use this third party as a hosting company for your media, I guess the easiest would be deleting the entries in your blog that speak of these illegal products, or if you don’t want the text itself but only the link, you may create a script that will remove it for you. As an example, if you use a WP Blog, WP allows custom fields. You can use one to indicate if the file is legal or not, and modify your templates in such a way that when the custom field says is illegal, there’s no link to the product. Yet, the article will remain and therefore the content.
Any change to your web is going to mean a change to your visitors number, whether is up or down.
You will have to look at your statistics to know where your traffic is coming from but no, there’s no way that you can keep the traffic if you remove an article. The url will not exist anymore.
You can minimize the damage by constructing a good 404 that informs the user why the page was removed, where he can go in your own site to find information about this particular product (as an example, if you built a new article with similar information and with no links to illegal content) and/or a search facilty.
Things like that.
This will do that part of that traffic will remain on your site anyway. How much? Percentages vary depending on how well you’re guessing the needs of your visitors.