When U.S. corporations want to merge or are subject to acquisitions (for example Oracle acquiring Sun Microsystems in 2009) it seems they must seek approval from the European Commission --- which is another jurisdiction.
Questions:
Countries, and supranational governments like the EU, have jurisdiction over companies that do business in their jurisdictions.
Oracle is technically not a U.S. corporation; it's a closely related group of California and Delaware corporations. Very few companies incorporate under U.S. federal law (I believe some banking corporations are required to, but don't quote me on that). Almost all companies are incorporated under state law.
However, if Oracle does business in Texas, it still has to obey Texas law. And if it does business in the EU, it still has to obey EU law.
Some laws make distinctions in some corporate matters between domestic corporations (incorporated under that state's laws) and foreign corporations (incorporated under another state's laws). But if you do business in a state, including an EU member state, you still need to obey that state's general laws, including antitrust law.
Short version: if you visit another country, you can't go around shooting people, then say, "your laws don't apply to me, I'm an American." Neither can a company, no matter where it's incorporated.
As for stopping the merger...any country where the merging companies do business can stop the merged company from doing business there if the merger violates local law. If this is a major, commercially important region like the EU, then failure to get EU approval will stop the merger. If it's a minor territory, the company will sometimes enter into an agreement to divest itself of local assets or entities. For example, if merging Oracle and Sun would create an antitrust problem in the minicomputer repair market in Laos, the merged entities would sell off either Oracle's or Sun's Laotian minicomputer repair division.
Chapka's answer covers the legal aspects that give the EU authority to impose their laws on US companies. However, there are also practical aspects around enforcing penalties. A court has no formal power outside its jurisdiction; a European court judgment (which is what happens if a company violates EU rules) can't be directly enforced in the US, because US law enforcement doesn't obey the orders of European courts. Enforcing those penalties can be done in two ways.
First, the EU can ask US courts to enforce the EU judgment; the odds that this works depends on the specifics of the case. In general, US courts are more likely to enforce a judgment from a proceeding they view as fair, and if it's compatible with public policy. There's a pretty good chance an antitrust case against Google or Microsoft would be enforced in the US; they do a lot of business with Europe, and antitrust is something the two places both feel is good policy. In contrast, Chevron is currently fighting enforcement of an Ecuadorean judgment on the grounds that it was obtained based on fraud and corruption, and is having a fair amount of success so far.
The alternative is to enforce a judgment on the assets the court does have jurisdiction over. Google and Oracle have many offices in the EU; they pass most of their revenue through Ireland and the Netherlands for tax reasons, but even without that they have real, legitimate offices in the EU. A judgment can be directly enforced against their assets there. To use the Chevron case as an example, Chevron transferred all its assets out of Ecuador, meaning that Ecuador can't directly seize anything.
