Enable software menu without virtual keys
LMT Launcher

Requires root access. 

I won't go into the details, but know that it doesn't replace your home launcher but gives you PIE navigation among other things, which comes down to this:


(Click image to enlarge)


You can set a PIE to Menu/Overview action from LMT app &rarr; PIE &rarr; select a PIE item &rarr; Menu
Make sure you activate the LMT service from the Settings and then you can test the navigation. 
For starters, PIE can be navigated from left, right and bottom of the screen. Swipe from the edge towards the screen and you'll see the PIE.
It has support for some limited gestures too. You would have to manually activate the feature from its Settings &rarr; Set Active Features.
And don't tell anyone: it even has a PIE pointer.