What are the real properties of an ordinary LED?
Internal resistance (in Ohms)
  


It's a Diode. Diodes don't have linear relation between Voltage and current, so they don't have a constant resistance, but a exponentional V/I characteristic. Diodes are non-ohmic.

Sometimes you model this behaviour as differential resistance \$r\$ instead of the fixed resistance of a resistor, \$R\$, subject to change over voltage:

\$r = \frac{dU}{dI}\$

Of course, there's also added static resistance due to copper losses and classical semiconductor (non-junction) resistance. It should be relatively small for usual LEDs during usage.

Notice that exponential relation between U and I implies that in reverse bias, a Diode pretty much isolates (aside from a minimal leakage current).


  
  Internal capacity (in Farads)
  


The capacitance of a diode depends on a lot of factors, mainly on voltage applied over its semiconductor junction. In fact, semiconductor elements are often used as adjustable capacitors by applying a variable bias voltage.


  
  Self-Inductance ( in Henries )
  


Well, like any device, the leads of an LED have inductivity. It usually doesn't matter much; you just don't feed a Gigahertz signal into an LED (different things apply for RF diodes!)

A lot of these numbers (aside from the inductance, which typically is dominated by the way you connect the LED to your circuit) should be available as diagrams in your specific LED's datasheet.