Depending on how you have things set up and their relative locations, if your inverter is not plugged into the grid, your energy collection system is needing to dump it's excess energy production somewhere, which is the theory for the grid tie. If you happen to be in an area where there is "off peak" usage, you might wish to discuss your desire with the power company. They may be more than happy to set you up with a smart meter that shuts off your house in high demand periods providing you have adequate system capacity to operate the important items in the house. You might even get some additional discounts as well. If you do this, you will want to have a dump load for your energy system for the excess production.
If you look at your inverter's instructions, there should be a section covering the theory of operation. All things being equal, In theory, if you are plugged into the inverter so all your loads are through it, you should be drawing from your energy system rather than the grid currently, except during your peak usage periods, or if your energy system reserves get low, then you will be drawing power from the grid via the inverter automatically.
Your largest consumption after AC is going to be for heating water (if electric water heater) and dryer (electric consumes the more electricity over a gas dryer.) then refrigeration. Adjusting these for optimal use will help reduce consumption year round.
Depending where you are, and what infrastructure is existent around you, if your water heater is electric- switching to gas, natural or propane might save some money long term. A lot depends on how much additional work might be required and if a "power vent" is needed to be added. Either way you go, if you are due for replacement of the water heater, most 12 year tanks have additional high efficiency foam insullation, and are worth the investment. There are timers available for electric heaters and you can pinpoint your peak times of when you need the hot water, and adjust accordingly. Or, you can go the alternate route and go with a tankless, or "on demand" electric water heater. Some options may not be available through a home center, so you might need to contact some specialty houses in your area or on the web.
There are many options and many variables. A local gas company can give you an estimated average usage per year for average gas appliances if you are not currently hooked up for gas. The other nice thing with gas is you can also set up an automatic generator so if there are problems with the power lines, say from storms, and it happens to be a particularly cloudy spell, or your wind system is out of order; having a generator that you can kick on to charge up the batteries and power the heavy draw appliances makes for a nice setup so you could go off grid completely if you chose at any time.
If you do go off grid, you want to have a dump load to consume the excess enrgy production from your system and convert it to something useful like water for heat, or for additional hot water production.