I haven't seen, or done, much by way of real scientific tests using blind ABAB type runs, and many of the mods would be hard to test that way anyway. But the bulk of the data I have seen tends to indicate that there's little difference, positive or negative in mpg coming from most mods, and that the differences that are seen could easily be explained by poor experimental controls and driver bias. Alternately, there could be small changes that aren't showing up for the same reason, just lost in the clutter.
That said, there are two things that do seem to have significant impact on mpg.
One, as mentioned above, is Fuel, specifically E85 conversion. E85 has been reported as reducing mpg anywhere from 20 to 33%; even if you assume some margin of error all in a negative direction it's impossible to deny that we're seeing at least 15% less mpg running E85. E85 is less expensive per gallon, but it's rare that it's sufficiently cheaper to make up for that kind of reduction. In theory 87 octane would be slightly worse mpg, 93 slightly more, whether that makes one or the other cheaper per mile would depend on the relative cost per gallon, but we haven't got any evidence that 93 really gives higher mpg at all. And it's possible that using 100% gasoline instead of the E10 you see in most pumps would also mean more mpg... but again, I haven't seen any proof of that.
The other is... harder to put into words. A car modified to be capable of producing half again as much power as it originally provided can still get the same mpg, within the margin of error, simply by driving it the same way under the same conditions. BUT adding potential power to a car has a tendency to encourage the driver to use that additional power. Accelerate harder, drive faster, you get worse mileage. Even if you never exceed the limits that the original car had, say you just install louder exhaust which you like to hear, so you floor it more often, you can spend more gas per mile. But using 180 hp to accelerate when you used to only be capable of 140 hp at most, you can spend that gas much much faster.
What that means is, that the driver is the most important factor in mpg. Power mods make it possible to get much worse mpg, and tend to encourage that, but if you can control yourself, the mods probably don't matter much either way, if at all.
Mods I haven't seen explored at all for the Sonic that might affect mpg would be things like streamlining, thinner tires, start-stop engine... none of those are mods that make more power.
Basically, if you are making 100 hp then you use a certain amount of gas to do that. In a stock car, that might mean you're at 75% of full potential, in a modified car it might only take 50% of your full potential, but that shouldn't really make any difference, and the data thus far seems to bear that out, more or less.
Streamlining, on the other hand, means that it might take only 90 hp to maintain the same speed that took 100 hp to maintain with the stock shape. That should mean it takes less fuel to drive around.
The reason E85 is worse is that ethanol has a lower energy density than gasoline, so it takes more volume to create the same amount of power. The fact that it has the equivalent of a much higher octane rating means that, if you can supply sufficient volume of fuel and enough air to mix with it, you have a higher amount of potential power makes it attractive, but it isn't currently an economical benefit. If petroleum prices rise and ethanol production costs drop (or if someone decides to monkey with the fuel tax system to massively favor E85) this could change. You'll always get fewer miles per gallon using ethanol, but you might get more miles per dollar... that doesn't seem to be the case now.
