Once frozen solid, transfer them to a container. I just pick up the edges of the parchment and use it like a funnel to pour them in a gallon size ziploc. I write the date on it to make sure I’m using the oldest first and then pop the bag back in the freezer. The cool thing about this is that the berries are frozen individually so you are able to just to get out what you need at any given time.
As far as strawberries go, I wash them, hull them and cut them in half. I then lay them on a parchment lined sheet pan and pop in the freezer. Once frozen through, I use the same method of storing in a ziploc. You could leave the strawberries whole, but if I’m blending them in a smoothie then halving them seems to work out better.
I also freeze peaches the same way. And I leave the peeling on. I just wash the fuzz off, slice them and place them on a sheet pan and freeze until frozen through. With peaches, they will retain their color better if you place them in a ziploc with lemon juice and shake them up so they are coated before placing on the sheet pan.