Bring water and strawberries to a rolling boil in a medium saucepan. Reduce heat to a simmer, continue to cook for 6 minutes. With a rubber spatula, stir the berries and mash them on the sides of the pan to release juices. Let the berries cool a bit and strain them with a fine mesh sieve or cheesecloth. If you like some pulp strain one time. If not strain 2-3 times. Let the strawberry juice chill in the fridge.
When the juice is cool, combine it with the rest of the ingredients in a large pitcher with ice. Serve with lime, strawberry slices and mint leaves.
For alcohol-free cocktails skip the vodka and add the same volume (1 1/2 cups) additional sparkling water.
Adjust sweetness to taste. Your berries may be really sweet or not so much.