To strain it either use a nut milk bag and squeeze into a bowl, or line a strainer with a thin kitchen towel over a bowl and squeeze the nut milk into the bowl. The more you squeeze the oats, the thicker and stickier the oatmilk will be. We preferred to stop squeezing once we noticed the liquid coming from the oats to be very thick, which we found made it have an unpleasant texture.
Pour into a jar and store in the refrigerator for up to 3 days, though it is better the fresher it is. Separation is normal in non-dairy milks, just shake it up before using it.