Parameters for Fitzhugh-Nagumo model of Action Potential
This is actually not the Fitzhugh-Nagumo model of the a neuron, however it is highly related to it. I believe the the Equation you have there, is capable of oscilations for any positive values of $\epsilon$, $C$, $L$. I generated this graph with the parameter values all set to 1.  Note how it is very similar to a sine wave.



I believe you where trying to write Van der Pol's equation here:
$$C\frac{d^2V}{dt^2} +\epsilon (V^2-1) \frac{dV}{dt}+ \frac{V}{L}$$ 
Note the subtle difference of multiplying by the first derivative. 
Here is again a image with all parameters set to 1



The Fitzhugh-Nagumo equation can be found on wikipedia here and on peer reviewed  scholarpedia here. For reference it is a two state model described by the equation:

$$ \frac{dV}{dt}=V-V^3/3-W+I$$
$$ \tau \frac{dW}{dt}= V + a -bW$$ 

A common value for the parameters are $a=.7$,$b=.8$,$\tau=12.5$ $I$ can be anything really, I used $I=.5$ to generate the graph below. Also note that the model wont spike if I below a certain value. The Fitzhugh Equation is is slightly more general, but does simplify to the Van der pol under the assumption $a=b=0$. Here is the graph of it with the constants I described.