For example would an everstone prevent trade evolution?
Yes, if the Pokemon is holding an Everstone, it will prevent its evolution and possibly its trade partner's evolution, e.g. when Shelmet and Karrablast are traded, if one or the other is holding an Everstone, the other won't evolve.
Other than it holding an Everstone you can't stop the evolution of the Pokemon by trade.
Source: Experience(literally went and tried it)