Heat 1 tablespoon of vegetable oil in a large skillet over medium heat. Fry as many of the limes as will comfortably fit in the skillet until the skin changes to a light golden brown. Repeat with remaining oil and limes. Set aside to cool. Wipe off the limes and cut each one into 4 wedges. If you have big limes, cut into 8 wedges.
In the container of a food processor, combine the chile peppers, garlic, ginger, and curry leaves. Blend into a smooth paste, adding a splash of oil if needed.
Heat 3 cups of oil in a wok over medium-high heat. Add the mustard and fenugreek seeds and fry until they pop. Stir in the paste from the food processor and simmer for about 10 minutes over medium heat. Remove from the heat and allow to cool slightly.
Add the lime wedges and vinegar to the oil mixture. Transfer the fruit to sterilized jars or bottles and pour in an equal amount of liquid, making sure the fruit is covered. Stir with a thin spatula to remove air bubbles. Cover with lids and rings, sealing the jars tightly. This pickle can be eaten right away, but improves after a few weeks in a cool dark place.