Combine strawberries, sugar, and a couple tablespoons of water in a blender and blend until completely smooth. Add a little bit more water, if necessary, to get it smooth (this will depend on how juicy your strawberries are).
Place a fine mesh sieve over a large glass measuring cup and pour the mixture through. Lightly press and stir the mixture through the sieve. Discard the solids. You should have around 1-½ cups of strawberry puree; you might not need all of it.
Add tequila, Grand Marnier, orange juice, lime juice, and 1 cup strawberry puree to the blender (no need to clean it out) and blend until combined. Taste and adjust ingredients as necessary. Serve in glasses filled with crushed ice.
Combine all ingredients along with approximately 2 cups of crushed ice in a blender. Process until smooth. Adjust the thickness by adding more ice. You might need a little bit more alcohol, since the ice will dilute it a bit. Serve immediately.
