The LEDs don't have a resistance, per se, what they do is to limit the voltage across them to some maximum, and if you apply a voltage source across them that exceeds that maximum, then you have a fight on your hands.
The fight takes the form of an LED (or series of LEDs) conducting very, very strongly, in an attempt to exhaust the power supply providing the excessive voltage. Either the voltage source is able to provide the resulting current, in which case the LED(s) lose the fight, and blow up, or the power supply is unable to supply that current, and blows up, or just provides whatever voltage the LEDs insist upon.
If you try to impose a voltage across the LEDs less than their combined maximum voltage, the LEDs don't have a problem with that, they won't fight. The resulting current is much lower. In this way, their "resistance" is not some fixed value, it varies depending on what voltage you try to apply across them. And because of this, you can't apply Ohm's law as you could for a fixed resistance.
In an analogy, the voltage source (power supply) is a strong rigid rod, with fixed length, and the LED is also a rigid rod with smaller, fixed length. Or perhaps it's a series of LEDs with a combined total length, glued end-to-end. By connecting the LED (or series of LEDs) directly across the power supply, you are trying to stretch the LED rod or compress the power supply rod to have equal length. Something has to give.
Actually, perhaps a better analogy for the diode is a piece of string of fixed length. It can be limp and floppy, adopting whatever length you want, until it's stretched straight. Then suddenly it becomes stiff, and opposes further extension.
A resistor is like a piece of elastic that is able to span the difference between the two lengths exactly, permitting the connection. The LEDs are able to keep their desired "length", the power supply is able to keep its desired length, and the resistor is happy to accommodate whatever the difference is:
simulate this circuit – Schematic created using CircuitLab
In this analogy, current is the "force" with which you have to stretch the elastic. They stiffer the elastic, the more force is require to span the gap, the more current flows. Stiffer elastic corresponds to lower electrical resistance.
I won't go into the details of how to calculate R, there are a million web pages to help you work that out. This answer is just to set you straight about why Ohm's law doesn't apply to the diodes, and why the resistor is necessary.