Many years ago my sister told me to use a straw to push the core from the berry, but every straw I'd tried was too flimsy, and the diameter too small, so my efforts weren't very productive.
This morning I got to thinking, as I looked at cleaning 4 lbs. of strawberries, "how can I make this easier?" I had an extra fat straw from the local coffee shop, so I gave that a go. The only trouble? Once the straw was full of cores, it was hard to push more of them from the berries that would follow, so I added a smaller diameter straw in the center, to act as a plunger. It worked beautifully.
Push the straw into the bottom of the strawberry, up through the leaves and out. If you miss the center, just pull back the housing straw, realign, and push again. When the core is in the straw, and pushed all the way through the berry, push the plunger, and out it comes.
Viola! Perfectly cored strawberries, with very little waste.