Photons (with no mass) have momentum.
Tachyons are not mass-less. They do not have "real" mass, where the word "real" is taken in its mathematical sense: the mass of a tachyon, if it exists, cannot be expressed by using a real number. You would have to use an imaginary number.
The traditional basis for imaginary numbers is designated by the letter i (or j if you are an electrical engineer) and is defined so that i^2 = -1.
The momentum would continue to be mv, except that the value of m is not "real".
However, the concept of tachyons requires that IF (a big if) you could get an observer to be in the same frame of reference as the tachyon (i.e., going faster than light), this observer would measure the mass of the object as "real", therefore the momentum would also be a real value.
This means that, in the context of Relativity, the mass of the tachyon is imaginary only for us, who are trying to perceive it from the "wrong" side of the light-speed "barrier". When it is observed from the other side of the barrier, it has real mass... and we are the ones with imaginary mass for the other observer.