You need to either 1) catch them when they are searching for an essay-writing service or 2) plant the idea and make the cold conversion. Adwords is best for #1. If you're not getting conversions on related terms, your landing page probably needs work... Adwords isn't a money pit unless you throw money at it aimlessly. Social is best for #2, plant the idea with a story from a student who used your service and got an A without the teacher making any comments, then lead them to sign up or convert. (Though I'm not sure you'll be able to buy ads for something like that as I don't do a lot of social stuff either - you may have to get spammy with it.) If you don't want to use Adwords or social I don't see how you're going to reach college kids and get them to convert for something like this.
