ExoticMatter is matter or equivalently, energy with negative mass hypothesized to exist as a result of solutions to Einstein's equations for GeneralRelativity. Evidence for its existence is seen in the CasimirEffect. It would allow for traversable WormHoles, WarpDrive, TimeTravel etc. Not the same as AntiMatter although perhaps there is a way to transmute from one to the other (neo-alchemy?). For more details see http://members.tripod.com/da_theoretical1/exoticfields.html
It is not equivalent to energy with negative mass, nor is it correct to refer to energy with mass of any sort in the first place. It is not even particularly related to the CasimirEffect (which in itself has only small, not large, experimental support), let alone does the latter provide evidence for ExoticMatter. It is not even a little bit related to AntiMatter, and it is about as meaningful to speculate about transmuting water to exotic matter: i.e. complete nonsense. AntiMatter may sound futuristic and cool and exotic, but all evidence is that it utterly normal in all regards except for its definition of inverted charge. There's no relationship to ExoticMatter.
If ExoticMatter turns out to exist, it might (not "would") allow for cool science-fictional uses of one sort or another, but then again, it might not. Most physicists would say probably not, even if it exists.
See Also TimeTravel, AntiGravity, QuantumMechanics, TimeTravelThoughtExperiment