According to the NRT website, Delta and Vietnam Airlines are both in Terminal 1. I suggest seeing if Vietnam Airlines can check your bags through to the U.S. If so, all you have to do is follow the signs for transit passengers. (Everyone walks down a long hallway, and then there's a point where the transit passengers and the passengers who want to enter Japan split up.)

Thousands of people transfer at NRT every day, so there must be some provision for those who have to collect and recheck bags. However, since transit passengers never officially enter Japan, I can't see why you would have to go through Customs and Immigration if you stayed airside.

Others may know more.