Well, I can see already that there are problems ahead for you. Having lived before in both Washington and Oregon, I know how cloudy it is for a large fraction of the year. The fact that you want to run a heater on colder days is an indication, that you need solar the most when your solar resource is at a minimum.
The components you've already got will make a good 24V system, but you desired application for winter heating is most likely to be a failure. In Southern California, you'll make lots of power with it, but in the PNW, don't expect to see more then 10% output from your panels. And electric heat is just about the worst application you can use solar for.
First, wire the batteries in two parallel strings of four 6V batteries. You can position them such that they form a U shape to cut down on the wiring distance. Let's call the four batteries in string #1 as 1,2,3, and 4. The four batteries in string #2 would be 5, 6, 7, and 8. To get the most equal charging, wire the positive terminal of battery #1 to your charge controller battery+ terminal, and the battery #8 negative terminal to your charge controller battery- terminal. It will look something like this, though the batteries in the pic are in a straight line, not a U. Use the 2/0 wire here. The over-current protection means either fuse or breaker, rated for 200A.
Once you have the batteries wired together, check the voltage with a voltmeter. It should be at 25-26V just sitting there.
Next, connect the +terminal of battery #1 to the battery + terminal on the charge controller. Connect the - terminal of battey #8 to the - battery terminal on the controller. Once the controller gets power, let it boot up and wait for the expected display to be shown. ALWAYS connect the controller to the battery first.
Now you are ready to connect your solar panels. What brand of controller do you have, and what is its voltage limit? Also, what is the Voc and Vmp of your panels? I'll guess the Vmp is ~30V, and the Voc is 37V? Two panels in series is the most you could wire if your controller has a 100V limit. You would wire the four panels 2S2P. That means two parallel strings of two panels in series. Use 4 gauge wire here.
Let's start with just two panels. The + connection of panel #1 goes to the + solar terminal of the charge controller. The - connection of panel #1 goes to the + connection of panel #2. Finally, the -connection of panel #2 goes to the -terminal of the charge controller. Again, just like the batteries, they can be fused or breakered, though for each string you need a 15A fuse/breaker.
You might want to cover the panels with a blanket when you first make your final connections, so a lot of current doesn't immediately start flowing. Once the connection is made, pull off the blanket and see how much power is coming in.
Finally, connect the inverter terminals to the battery strings. Use the same 2/0 cable to connect the inverter +/- to the same battery +/- that everything else is connected to. Once the inverter is connected, turn it on, and plug in a small load, such as a single light bulb lamp. Once you see that working, start plugging in larger and larger loads to see how the new system performs.
Once you know that the minimal system is up and running, you can connect the second solar string to the same terminals to bring it up to full power.
Good luck