I'm trying to delete a trigger off production, but all my efforts to do so have been met with failure. My most recent attempt should work, but the IDE is first asking me to upgrade my version of the code from production. What will this do to my data? The comparison looks like the new version is completely empty, does this mean all my metadata in these objects are going to disappear?
I believe Eclipse is saying that the project must be updated to the latest version, not the server code. Which means your Eclipse project will be refreshed from the server to match what has already happened to the server.
You can't upgrade your production server to Summer '14. That upgrade just happens when Salesforce wills it. And it has already happened.
If you're nervous (like I was the first couple of times Eclipse said this to me) you can abandon your existing project and just create a new Eclipse project pointing at the same Org.
Then you can go ahead and perform your delete.