Set up security groups / NACLs that block the relevant ports, and using IAM make sure users don't have rights to modify the firewalls. You might be best off whitelisting only the ports / hosts you need the servers to access. Sometimes that's difficult, for example if you need to contact Windows update there can be a large number of hosts to contact. You should whitelist only the AWS services you want people to access as well, using Service Control Policies, and make sure you give people least privileges to do their job.
However I think you'll find people who want to steal data will find a way. Putting data to S3, Route53 DNS, via one of the many many AWS services, to a server running on a non-standard port, downloading via the console, there are many ways to exfiltrate data. All you can do is make it more difficult, and set up alerts as best you can so you know when it's happening.