How would I measure the gallonage of this pool?

You could divide the surface area into geometric shapes. Measure the shapes and determine their areas to get your total surface area in square feet. Multiply that by the average depth to get approximate cubic feet. Multiply by 7.48 to get gallons.
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Google Maps. Zoom in as far as you can. Right click at one point on the edge of the pool and select "Measure distance". Then go around the pool little by little left clicking until you finish back on the 1st point. It will give you the total perimeter and the total area. Next you need the average depth. Take the shallow depth and deep depth and average them and assume that's it. Now multiply the total area from maps by the average depth (in feet). That should give you a volume in cubic feet. Multiply by 7.5 (actually 7.48, but 7.5 is close enough) to get gallons. That'll get you in the ballpark. The big guess is the depth.
 
How precise do you want. For pool purposes, accurate is +/- 10%. Precise is much harder. Add a known quantity of a chemical, like chlorine. One pound of chlorine (the average amount in one gallon of fresh 12.5% liquid) will raise the ppm of 10,000 gallons by 10. Add it on a cool, preferably overcast or shady, day. Circulate for about 2 hours and use an accurate test kit. Test before adding then after a 2-hour run. Draw water for the test from about 18" below the surface (invert vial, right it when you reach as far as you can). If it went up 10ppm, you have 10,000 gallons.

You can take that example, add your own readings and get very close (precise?). Then, after a dry North wind in California the next day you will have lost a few hundred gallons to evaporation.
 
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