The movie starts weird and gets weirder, never particularly interested in making any sense at all. Wikipedia classifies it as "dark fantasy science fiction horror," and it has elements of all these things. If the name "Don Coscarelli" means anything to you, this lack of sense will probably be unsurprising: this is kind of how he makes movies (although at least "Bubba Ho-tep's" plot was mostly coherent). Our narrator is David Wong (who isn't Asian), who works with his friend John as a psychic investigator. They've taken a drug called "Soy Sauce" that makes them become unmoored in time, and also able to cross to alternate dimensions.
I was never clear whether "Soy Sauce" was the cause of the problems or the solution, or possibly both. It was apparently supplied by the aliens as precursor to invasion, but it was also what let David and John solve the problem. Or maybe they solved a different problem entirely. Coherence really isn't a critical part of the story structure here.
I can't really recommend watching it, and yet I don't regret watching it: it was kind of fascinating. If Coscarelli ever gets his shit together about narrative coherence, he chooses decent actors and makes his subject matter bizarrely compelling. He still wouldn't have a genuine "hit" on his hands (his stuff is just too damn weird), but he might break even at the box office.