I would say that your options are pretty limited, but it also depends on what your expectations are, exactly.
First, it's unclear if you want to measure or calculate the calories.
The "calculate" part is much easier to cover: you can't. Calculating calories only works when you are combining ingredients, then it's simply the sum of the ingredients. But when you're taking away part of the ingredients, there's no way to calculate how much is left. You'll have to measure it empirically.
Your suggestion of approximating by the weight of discarded oats isn't workable. You're soaking your oats, so you'll probably discard more weight than the weight of the dry oats you're putting in. This doesn't mean that your milk has negative calories, but simply that you're discarding some of the water along with the oats - and you don't know how much.
As for measuring, then it's unclear what you mean by "intuitively", since measuring is the opposite of intuition. If you're asking for a method that is doable under home conditions, the answer is "maybe".
There certainly are ways to rig a simple calorimeter at home and use that. It doesn't even have to be the "bomb" type. You can find many descriptions around the Internet, intended for kids' science projects and the like. You'll run into several problems:
- It will require a lot of time investment on your side
- A simple homemade device will probably be rather inaccurate. You can of course try to calibrate it, by using published calorie tables and foods which aren't likely to vary much from one sample to the next, such as plant oil or sugar. But you'll probably have to do a lot of experimentation series until you have an inkling of how reliable your measurements are.
- Your oat milk is liquid. You'll have to dehydrate it completely before burning it in a calorimeter. As you don't have access to industrial methods, you'll have to choose a slow dehydration method - during which enzymes and bacteria can change the composition of your oat milk (although this will likely cause a shift in the macronutrient composition rather than a big change in total calories)
- It's unlikely that you're able to produce consistent results between batches of oat milk. So even if you can overcome the practical problems of creating a measurement, you'll end up with a somewhat broad range. Although that last part is inherent in calorie counting anyway, and the major databases simply list an average value.
It's of course up to you to decide if you want to invest all the time needed just to get some approximate results. If I were counting calories, I would probably simply opt for counting the calories in the oats as an upper limit, and call it a day.