The difference between most European and North American home styles lies in brick colors or the shapes of the roof because the climates for which they were designed are similar. A home for sale has to be able to withstand the same four seasons with their gusty winds, driving rain, heavy snow, and baking summers as a German cottage. However, Asian climates are entirely different and their homes are designed to match, giving rise to vast differences in architecture from what we're used to in North America and making Asian homes the epitome of exotic in Western eyes.
You don't need to equip your cell phone with a global SIM card and tour the Asian countries to find examples of their architecture, because Asian immigrants have brought their style to North America with them. In the "Chinatown" areas of big cities, especially those on the West Coast like Vancouver or San Francisco, you can see brightly colored roofs of lacquered wood and gold and tall wooden gates leading to zen rock gardens. However, these can only ever be replicas of the real thing, because the light woods and delicate screens they would have used in China and Japan would never survive the climate of North America.
Therefore if you want to see or own an Asian style home, your best bet is not to hire a construction company with a foreign worker program to replicate you one, but to buy yourself a pocket translator and move to Asia. Go to China and marvel at the sweeping, gorgeously carved roofs with their open-air corridors and delicate paper lantern accents. Find a pavilion on a placid lake or a house that rises in steps up the side of a steep cliff face. Chinese home styles often feature an enclosed courtyard, so be prepared to see gorgeous flowers growing through every interior window of your house.
Japanese architecture is similar to Chinese, especially in the number of ways that they are different from your standard chrome-and-glass condos. The climate in Japan, and in Asia in general, is fairly congruent with that of China, so many of the architectural features, such as the sweeping roofs, light building materials, and propensity to include open-air corridors and courtyards, remain the same. However, there is much less space in Japan, so the emphasis is on building up, not out, especially in modern Japanese architecture. Even many older Japanese homes were built upon stilts or pillars in order to make a swampy parcel of land livable.
China and Japan aren't your only options, though they are the largest and most evolved. Korea, Thailand, the Philippines and other island nations, are all options with similar architectural bases. If you do end up modeling your North American home after an Asian style, make sure you hire consultants with real estate training and a background in architecture, as they would know what would stand up in our climate and what wouldn't.