Toss the watermelon, diced strawberries, sugar and salt in a large bowl to blend. Let stand until the sugar dissolves and a syrup forms, stirring occasionally, at least 15 minutes and up to 30 minutes.
Working in batches, puree the fruit mixture with the tequila and 2 teaspoons of the lime juice, combining each batch in a large pitcher. Stir to blend. Add more lime juice if desired. Refrigerate until very cold, at least 1 hour and up to 3 hours.
For the garnish: Thread 1 strawberry, 1 lime wedge and 1 watermelon cube onto 6 skewers. Divide the agua fresca among 6 chilled glasses. Stick a skewer with garnishes into each drink and serve.