Is there a way to determine what is powering the content behind a URL? I have a relative URL in a large site that I inherited: /my-url. 

For the life of me I can't find the View, Module, or other content that shows how to edit this URL. I've grepped the code base, and searched the database, but can't find it. 

How can I tell how this URL gets edited? Is there some kind of search modules/views/blocks by URL?
You could try looking in the menu_router table, where the path column contains values like node/%/revisions/view. Also, the url_alias table has a source column (to check against the menu_router table) and the alias defining a path like /my-url.

I also use TextWrangler and PHPStorm to inspect my code. You could try to search.