It depends on whether you are just putting LEDs in the sockets, or if you are purchasing a unit with a plug that is designed to fit the socket. The pre made/designed ones should work without a resistor. If the signals do not work, then you may need either the resistor or a relay. The manufacturers do not always let you know if they will work properly.
If you are using a single LED for each application, depending on the rated voltage you will have to run a resistor. If they are rated at 3.5 volts, you can run 4 in series to drop the 13.5-14 volts the system is designed for. If you use one, the resistor should be about 570 ohms, or slightly more. There are some high output LEDs which are designed for 7, and 12 volts. You can use 2 of the 7 volt units in series, or one of the 12 volt units by it self. You may need a resistor to activate the relay. You would have to experiment with the size so that you do not starve the LEDs.
Its not as much voltage as it is current. Yes its true running 4 3-3.5V LED's in series will give about 12-15V of driving voltage but the current is going to be A LOT less than with a light bulb, hence why a resistor is needed with the stock flasher unit. With an aftermarket electronic flasher unit its not needed as it causes the circuit to blink at a set speed regardless of current draw. A standard flasher unit uses the bulbs as part of the flasher circuit, that's why if a bulb burns out the flash rate becomes slower on the side that has the burned out bulb. If you put the LED's in without a resistor in series to increase the current draw the LED's will flash too quickly or not at all. - Peter
Some of the "ready to install" LEDs may have a resistor in them already. They do not tell you if they are designed correctly or not. The use of the resistor may drop the voltage excessively for series mounted LEDs, depending on the necessary value of the resistor. If the resistor drops the voltage too much, the LED will not light, or will light, but it will be dim. You would have to experiment with the resistors and LED combinations. You also have to consider the wattage of the resistor, so that you do not fry it.