This isn't exactly the same as Eclipse from your description, but Visual Studio has some similar features out of the box (I've never used Visual Assist X, but it does sound interesting).
The Find ComboBox in the toolbar ends up being a sort of "Visual Studio command line". You can press Ctrl+/ (by default) to set focus there, and Visual Studio will insert an ">" at the beginning of the text (indicating that you want to enter a command instead of search). It even auto-completes as you type, helping you to find commands.
Anyway, to open a file from there, type "open <filename>". It will display any matching files in the drop down as you type (it pulls the list of files from the currently open solution).
To quickly navigate to a function, in the code editor press Ctrl+I to start an incremental search. Then just start typing until you find what you are looking for. Press Escape to cancel the search, or F3 to search again using the same query. As you are typing in the search query, the status bar in the lower left corner will contain what Visual Studio is searching for. Granted, this won't search across multiple files (I've never used Eclipse much, but that sounds like what it does from your description), but hopefully it will help you at least a little bit.