How to connect a 2 wire 220v power inverter to a 3 wire 220/110v house
I’m going to assume you’re in North America, with split-phase 120/240 volt service.

The answer is you can’t, at least not directly.  If you were to connect the inverter to your two hots, it would be the equivalent of losing your neutral. Search this site or the web for “open neutral” and you’ll see how dangerous that is.

In theory, you could use a 1-to-1 isolation transformer, with a center-tapped secondary to provide the neutral. Make sure it’s rated for the voltage and current (not to mention the line frequency) of the inverter.

Let’s talk about other issues.

For one thing, I wouldn’t be caught dead with that rig connected to my house! Read about all of the poorly designed and manufactured crap coming out of China these days. You are literally playing with fire.

Second, you say this is an off-grid inverter (glad you’re not trying to use a grid-tie inverter). Are you actually off-grid or just looking for backup? How are you planning to tie in to the house if you are normally on the grid? Flipping off the main breaker and flipping on the breaker to the inverter without any kind of interlock is dangerous and clearly against code. Either use a generator transfer switch or an interlock.

Last of all, don’t expect your homeowner’s insurance to be very happy when you make a claim. This rig is most likely not legal to be installed in the US.