In modern physics, it is well understood how particles can travel with superluminal velocity without violating special relativity or causality.
The MINOS experiment a few years back already found evidence that neutrinos may move faster than the speed of light c, namely at 1.000051 (+/- 0.000029) c. The Supernova 1987A in the Large Magellanic Cloud 168, a thousand light-years away, indicated at most a tiny increase over the speed of light. Some 23 neutrinos were captured over a span of 13 seconds, arriving 3 hours earlier than the first light was captured.
In fact, this time difference is mostly due to the neutrinos carrying most of the nova’s energy (in a type II supernova) through the outer layers of the star while much visible light emerges only after the shock wave from the stellar core collapse reaches the surface of the star. OPERA indicated a velocity of only one part in 100,000 exceeding the speed of light (c).
Looking at all these experiments, the superluminal speed is going down along with the total distance over which the neutrinos have traveled. This indicates that they just traveled a short distance (x) faster than light, after which they slowed down and traveled further with a velocity just under the speed of light. The longer they travel afterward, the less the initial short distance x of initial superluminal propagation is noticeable as an increase of the average velocity v. The average v equals total travel time divided by the large total distance D, so it seems that there is only a small increase over light speed.
Our three dimensional universe may also be due to a three (or more) dimensional membrane inside a higher dimensional, so called bulk space. This is called “universe on a membrane” or short “membrane universe” (MU). In the MU scenario, our light velocity c is the maximum velocity of excitations inside the MU membrane, the latter being the very reason for why the MU universe observes Einstein relativity within it. That velocity c may be very small compared to the maximum velocity of particles that are not bound to our MU membrane, those that speed freely through the bulk space with perhaps, as indicated by the OPERA data, at velocities thousands of times the speed of light.
(For instance, imagine ocean waves. The maximum velocity for ocean waves is much lower than the maximum velocity for its associated splashed water, which is no longer bound to the ocean waves and is, essentially, moving in a higher dimension.)
However, though neutrinos have been shown to move faster than than light, the primary question still remains in using them as a viable means of propulsion for an interstellar vehicle.
E = p/c (Energy of neutrino or photon = momentum of photon/speed of light) for photons and neutrinos. That means for every 300,000,000 joules of neutrinos you fire out the back of your ship, you can push 1 kilogram of mass from 0 to 1 meter per second. So a ship that weighs a thousand tonnes wanting to change its speed by 100,000 meters per second needs to emit neutrinos with a combined energy of ~3*10^19 joules (~7 gigatonnes TNT equivalent). Thats a lot of neutrinos.
Ah, upon further thought, it wouldn't work anyway; even if you could influence the direction in which the decay products from a nuclear interaction go in the decay's wake, the neutrino is a third body, hence it would still only be confined to spherically symmetric possible paths.
For instance, you could make it more likely (by a small amount) in beta decay for the electron thrust to issue in one particular direction, the neutrinos would then be more likely to emerge in a disk (very nearly) perpendicular to the path of the beta particle and daughter nucleus. A disk is spherically symmetric, so there would be no overall thrust in any one direction.
You would instead just eject the electrons from the back of the engine, but this isn't worth it; electrons are Fermions, which means you can't have very many of them close together at any one time, so by neccesity the thrust must be vanishingly small or any increase in efficiency you might gain you could get just as well from a conventional ion engine, for much less trouble .
Alpha particles sound more promising; they are Bosons, so perhaps if you were exceptionally clever with the design you could compress a mass of unstable nuclei in order to make spontanius emission on a large scale - an Alpha particle Laser so to speak (an Aaser? xD). However, this is like a gamma ray laser but much, much more difficult; they work on paper, but in practice the resonance effects are so delicate that the slight variations in speed of the nuclei emitting the gamma rays dilutes the probability of stimulated emission resulting in usable thrust.
It appears unworkable to try to get ordered behavior from groups of tiny, immensely compact and complex nuclei.
We may need to employ electrons for thrust instead of the smaller sub-atomic particles. I'm not sure if neutrinos can ever be contained, contained in sufficient quantities, and then emitted in a predictable and controlled thrust. Lastly, I don't see any advantage whether or not these neutrinos offer any super-luminal speed after being ejected from space faring vessel because the energy has already been expended in the ship's change in momentum.