2008 Legacy - oil level seems to be rising and smells like gas and thinned out, running poorly. No check engine codes. 

Can I unplug the electrical connector to the injector as a test?  Or do they just internally whether they are plugged in or not?

A leaky injector will leak regardless of being plugging in electrically or not from what I understand. It’s worn injector components or grit that holds the injector open allowing the residual fuel pressure to leak out. 

You could bench test this easily enough. Build up pressure with an external efi pump, shut it off and watch for leaks with a cup under the injector to catch any fuel (this will give you an idea of how much is leaking too).

Also check the injector wires to ensure there’s no current keeping the injector open after engine shut down. That would be a long shot but anything is possible.