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If you remove the URLs using the tool they will stop ranking as soon as Google trys to crawl the pages again. This may take a little a little while depending on how many pages are currently linking to the pages that you want removed. Unfortunately there is no way to get them removed with immediate effect, though it is unlikely that a few duplicate title tags will have a huge effect on rankings.

If the content isn't there, you can setup a 410. That will tell the search engines and users that the pages are gone for good. GWT will also show broken links to your site as well. So you will want to distinguish between the inbound 404s and the pages that are no longer there. There's a possibility that the pages have been gone for so long, they're no longer indexed. So I'm not really sure how much good a 301 will do from a link perspective. However, if you have access to referral data - you may find some of those inbound 404s are worth redirecting to a relevant page.