In a small bowl, combine the garlic, orange juice and 1 teaspoon lime juice. Whisk in the olive oil; season with salt.
Using a food processor, puree the avocados with the remaining 3 teaspoons lime juice and season with salt; transfer to a small bowl. Clean the food processor.
Line a baking sheet with paper towels. Fill a large pot with enough oil to reach a depth of 3 inches; heat until it registers 335 degrees on a deep-fry thermometer. Using the food processor, puree the plantains with 1 1/2 cups corn. Transfer to a medium bowl and stir in the remaining corn kernels, the baking powder and 1 teaspoon salt.
Working in batches of 6, spoon heaping tablespoonfuls of batter into the oil and fry until puffed and golden, about 3 minutes, allowing the oil temperature to return to 335 degrees between batches. Using a slotted spoon, transfer the hush puppies to the prepared baking sheet to drain; season with salt. Serve hot with the orange-garlic and avocado dipping sauces.