The Wikipedia page has a lot of cool information, and some pretty pictures, though a lot of it's over my head.
What kind of system would we need to be created?
Gravity waves are created by anything with mass moving. A sinusoidal gravity wave would naturally form from a mass moving in a circular pattern, such as a star or planet orbiting something else. On a smaller scale, you can put a bucket on a rope and swing it around your head. Note that the motion can't be spherically or cylindrically symmetric, so a disc or sphere spinning in place won't work. See this answer for more details.
To make a standing wave, you need to create a second wave with the same period somewhere else. (I think one period just has to be an integer multiple of the other period, but I'm a bit rusty.) Note that this will only give you a standing wave in a straight line between the two systems in 3D space. In other directions, you won't have such a neat symmetry.
Here is a cool applet that shows you interference in 2D waves. Note the standing wave between the nodes, and the moving waves everywhere else. 3D waves are more complicated, but similar.
Creating a region (volume) of space filled with standing waves is hypothetical possible, but I have no idea how you'd even start with gravity waves. You can't reflect them, and any giant space-shell made of orbiting planets would collapse onto itself.
Can a system be engineered to cause a standing wave resonance with gravity waves?
Basically you need to do one of two things. First, you can measure the resonance of your third system, then make the standing gravity waves oscillate at the same frequency (or a harmonic frequency). Second, you can measure the frequency of your gravity waves and engineer a system to have the same resonant frequency.
What can we theoretically accomplish by creating a standing wave?
I'm sure there's something out there, but the only thing I know of where you want resonance is a musical instrument. In other cases, you use resonant theories to avoid your system resonating with any high-amplitude local waves, so it doesn't blow up or fall apart.
How much energy would it take to create a gravity wave never the less a standing wave resonance from gravity waves?
Any finite amount of energy can produce a gravity wave or standing wave. However, swinging a bucket over your head produces a gravity wave of practically zero strength. For your gravity wave to produce a non-negligible effect, you need a lot of energy. I don't know that much about the subject, but we're talking really dangerous things like binary neutron stars or black holes. Things you aren't likely to just set up real quick for an impromptu jam session with the band.
This is why it took so long to get any real evidence of them. Almost nothing in the nearby galaxy can produce strong enough gravity waves to detect, and the ones we detected were still tiny.