The problem with this is mostly that since neutrinos interact so weakly with everything else, it’s really hard to do anything interesting with them. Even if you got them to interact in such a way as to do calculations, at some point you have to convert that to non-neutrinos to get the output, and you’ll miss the vast, vast majority of them when that happens.
Also, since neutrinos have such a low mass, even the tiniest of energies are enough to send them zooming off at nearly the speed of light, so it’s really hard to keep them contained in a reasonable-sized computer.
And their oscillations have no bearing on their suitability, or lack thereof, as a propulsion system. For some purposes, there are advantages to your rocket spew consisting of very light particles, and if we could cause them to be preferentially emitted in the right direction they might be suitable for that, but we wouldn’t have to worry one way or the other about oscillation.