offense outside US

Can an offense committed be investigated and tried in US by a state/federal court. Can someone sue another person for something happening outside US

Correction! Meant can an offense outside US be investigated and tried in US.

It depends on the offense and what is being charged. For example, murder of a US citizen in a terrorist attack by a foreign national can be prosecuted in the US. And if the act is part of a conspiracy, with any US connection, it also can be prosecuted in the US.

The offenses like theft, fraud etc with absolutely no US connection at the time these happened

The offenses like theft, fraud etc with absolutely no US connection at the time these happened

More than likely, you would be tried in the country in which it happened. I would much rather be tried in the US than any other country, ever heard of canning??? (that was not tried in US)

You can be sued civilly in the US for a civil wrong that occurred outside of the US.