Is there a minimum energy content of information, other than 0 Joules? Lets say I want to send the bit string 010110 to someone. Is there a theoretical lower bound on the energy needed to do this?
 A: See e.g. Landauer's principle  and capacity of noisy channels.
Not everybody agrees with these limits, but to me they seem fairly reasonable based on relatively straight forward noise arguments. In an ideal world (i.e. temperature T=0), there is no lower limit for the energy needed to store a bit, in the real world, however, noise will interfere and the third law of thermodynamics guarantees T>0, i.e. that there is always noise. As a consequence, one has to have enough energy (and in case of information transmission, enough power) to be above the noise floor, to make a distinction between ones and zeros.
None of this, however, has anything to do with superluminal information transmission. The people who use dispersive systems to attempt to produce superluminal phase velocities for information transmission have not been able to demonstrate, that they are actually superluminal (albeit, in my opinion, some may have demonstrated, that they don't know how information is defined in physics).
A: Is there a minimum energy content of information?
Carl Witthoft's answer gives us a key hint: in terms of energy efficiency one can't really do better than using photons to encode bits. 
A photon residing in a container of linear size $R$ has minimum energy $\Delta E \approx \hbar c / R$. By increasing the size $R$ one can reduce the energy per bit below any desired value. Still, the number of bits $N$ one can store using total energy $E$ is limited by the product $E$ times $R$: $$N < \frac{E}{\Delta E} \approx \frac{E R}{\hbar c}$$
This, in essence, is the Bekenstein bound, an upper limit to the information that can be contained within a given finite region of space which has a finite amount of energy.
A: This may not be the best way to look at the problem,  but:
Suppose you send one photon for a "1" and no photon for a "0" according to some prearranged clock.  What's the lowest possible photon energy?  The answer, of course, is "asymptotically approaching zero."    
Not that I'd like to build an antenna capable of detecting a photon with $\lambda > 1$ parsec. 
