How much protein powder
You should try to balance it out to match the amount of food you are trying to eat. So if you are shooting for 3 oz and the protein powder is going to net out to 1oz then mix it with 2 oz of oatmeal. Now what I do for protein oatmeal is I make a protein shake with unsweetened almond milk and then put my regular oats in it over night. So if you are making 1/3 cup of oatmeal you might want to put that 1/3 dry oatmeal in about 1/3 to 1/2 cup of protein shake mix it well and let it sit in the fridge over night. It works out quite well.
I also sometimes mix a half a scoop of chocolate protein powder with 2 tbsp of peanut butter for a post-workout snack and sometimes throw a tablespoon or so of dry oatmeal and mix it together.