Were they still allowed to fight for the United States military?

The 442nd Infantry Regiment ("Go For Broke") was made up almost entirely of Japanese-American volunteers taken from the internment camps or Hawaii. It is generally considered the most decorated unit of its size and length of service in American history.

Unless you're talking about Nisei in the military before WWII began? If so, there were few. Those that were mostly were in the Hawaiian National Guard... and they got disarmed a couple of days after Pearl Harbor. Not overly long after that, all Japanese-Americans in the US military were classified as "enemy aliens" and removed from their positions.

Eventually there was a call for volunteers to form a Japanese-American unit. 10000 Nisei from Hawaii volunteered, along with some from the internment camps, and the rest, as they say, is history.