I searched my name in a search engine and there are links that show up for social sites I once had accounts for. I have since deleted them a long time ago but the links are still there even though the lead to a page saying that the account has been deleted. What can I do to get rid of these?

There is nothing you can do... eventually they will disappear from the search engines, "maybe".

Just another lesson of once its out on the net... its out there, sometimes for good. When you consider the bigger search engines are on the verge of dealing with Petabytes of info and not terabytes, you can see why a few things a mere few bytes can not be removed..

You can't put the cat back in the bag once its out.

Particularly since you don't own that info.