Fun. Good luck.
To measure the difference, you'll probably have to use some pretty big averages over the same route, or very similar driving. There are a ton of variables to control - most important one is temperature and how you drive. You'd want to make this as reproducible as possible.
If you drive the same route every day - isolate the kwh/mile values for that first time in the morning trip. I'd keep track of the outside temperature for those days. And probably split them between above 45 degrees and below 45 degrees. You're probably also calmer in the morning (I bet if you look at your history for the same commute, you'll see lower kwh/mile use in the morning than at night coming home). You'll probably need a good 20 or 30 commutes to get a good number.
Then when you get the new oil, do the same thing. 20-30 more commutes.
Here's the tricky part, you'll have to figure out the variation in each of the data sets, before and after. Calculate the standard deviation of both sets (spreadsheets have that function, so do some calculators). Then multiply the standard deviation by 3, and that number tells you if the difference you are seeing is significant. The more replicates you do, the better the standard deviation number.
More than likely, the variation of the two data sets will be so big, you won't be able to tell if there is a difference. It might look like the new oil gets 5 kwh/mile better economy, but when you factor in the variation of the data, the difference is insignificant. So there really was no change. On the other hand, maybe you will see a real difference.
The worst thing you could do is try to pair data, before and after, with single data points. More than likely you are going to try to drive more gently after you make the change, trying to get the result you want. You'd do that subconsciously. And it is perfectly normal.
The other approach is to just use your big grand averages to see if there is a difference, over a lot of trips and time. The biggest problem with that approach is temperature. You won't end up with data collected with similar temperature patterns. Well, unless you live in LA and it is 70 degrees all the time.
Given the range of the car, you probably are driving the car in similar areas. If you all of a sudden started driving in San Francisco, and you used to drive in flat LA - well that would be a difference. Generally you're driving similar terrain day in and day out.