Is the mass of Tachyons real or imaginary? I have always considered quantities like mass, charge, momentum etc. to be real quantities as them being imaginary doesn't make much sense to me.
But for tachyons to exist, they should have imaginary mass compatible with special relativity. Or their rest mass should be imaginary for their masses to be real. So is the mass of tachyons real or imaginary? And if it's imaginary, can there be an imaginary charge, momentum etc.?
 A: First let's clear up the possible confusion about rest mass and mass. All working physicists these days define mass to be the same thing as what used to be referred to as "rest mass" back in the 1950's. The modern convention has slowly filtered down into textbooks and is now a universal standard except in popularizations.
The definition of mass is $m^2=E^2-p^2$ (in units with $c=1$). Mass is not additive.
A tachyon has a spacelike world-line by definition. By symmetry, its energy-momentum is parallel to the tangent vector to its world-line. Therefore its energy-momentum is spacelike, and $m^2<0$.

And if it's imaginary, can there be imaginary charge, momentum etc? 

We don't do general relativity on complex manifolds, we do it on real manifolds, so for compatibility with GR, the energy-momentum must have real components.
I'll leave it to others to discuss whether imaginary charge makes sense. This might depend on what you pick as your definition of charge, whether you're talking about classical or quantum physics, and what kind of distasteful outcomes you are or are not willing to accept.
