I'm still confused about this issue. My example would be if I live in the U.S, but my content is hosted overseas, can the U.S. govt. successfully still file a lawsuit of something?
Most countries take copyright issues seriously and yes you can be served with a C&D from a U.S based party. Most of Western Europe would comply with copyright violation.
In your example of living in the US, it would not prevent you from getting in trouble. In fact, hosting the site in another country might ensure a harsher sentence/judgement if they were to come after you. The reason for this is that your action of hosting the site offshore (presumably in a country with lax copyright laws) would be taken as de facto evidence that you knew what you were doing was illegal and you tried to circumvent the law. It takes a lot more than merely hosting the site in another country to avoid prosecution. Of course, criminal prosecution is unlikely, though not impossible. Having the site hosted overseas would give you no protection from civil lawsuits.