How Do I Switch Between Multiple Eclipse Windows (in "Split Screen" Mode)

By default, its Ctrl+F6. However, its useful if you map you keys to Ctrl+Tab to switch between open editors like Windows.

You can change your preferred keys in Window>Preferences>General>Keys and change "Next Editor" to any key of your choice(Ex: Ctrl+Tab). Hope this is what you needed.

This can be achieved easily if you are using Vrapper in Eclipse. Vrapper is a Vim plugin for Eclipse. If you are trying to maximize your productivity in Eclipse like we all are, it's well worth the try.

Once you got it installed, check out the Split Editor Plugin for Vrapper. You can then create splits on the fly and switch between them using the standard Vim shortcut: Ctrl-w w

Bonus: don't forget to maxmize your editors using Ctrl-m.
If your editor ever loses focus for some reason, regain it by pressing Ctrl-F12
Finally open any file in your project using Ctrl-Shift-r

Edit from anula comment: A useful thing to mention here: Ctrl-w by default binds to closing window, so if you want to use it as in Vim you need to first go to Window->Preferences->General->Keys and unbind "Close".