Thus, all of the above fish can interbreed. They all belong to the genus Poecilia.
Do Platies Crossbreed?
Yes, swordtails and platys are part of the genus Xiphophorus. Thus, the species can interbreed.
Platies are Xiphophorus maculatus
Swordtails are Xiphophorus helleri
Platies that are Xiphophorus maculatus cannot interbreed with Guppies which are Poecilia reticulata and vice versa.
Lastly, keep in mind that these fish are prolific breeders and will try to mate with other live bearer fish in the tank (especially male guppies). But, there will be no fertilization and thus no fry from the attempt to mate.