Travel between Germany and Poland by train

Wow. Interesting question, and one we don't get here very often.

• As a Polish citizen, you are allowed to enter Germany and Poland and to cross the border as often as you like. The problem is proving your Polish citizenship since you have no passport. I think you are required to have a national ID card, too, I don't know how that applies to expats.
• As a NATO soldier, you are allowed to enter NATO states with your military ID instead of a civilian passport, provided you do so under orders. You will be on leave. I presume that your unit knows you want to cross an international border during your leave.
• The comment by Suncatcher is right that there are no systematic immigration controls, but there are random spot checks and failure to get this right could get you into trouble with the Army.

My suggestion would be to ask your unit staff. They should probably be told that you're going to Poland, so you can ask the documents question as well.

Follow-Up:

• The Schengen area has abolished systematic internal border controls, but not the requirement to carry valid ID documents for crossing borders or to present them to the authorities on demand. The forum answer that it has to be a passport is right for a US civilian, but you are neither.
• You have orders to go to Germany, which makes your US military ID valid in Germany under the Status Of Forces Agreement (SOFA). You should ask somebody who knows military law how travel on leave is handled, because you have no orders to go to Poland.
• I agree with the guess that you're unlikely to be asked for papers, and if so your military ID would probably suffice. But if, say, you break your leg or you get into a car accident, questions about your identity and your unit might come up.
• There is definitely some profiling going on regarding "random" spot checks. Not just racial profiling and not all of it illegitimate -- young men coming from the Netherlands are checked for drugs more often than elderly ladies, businessmen going to Switzerland are checked for cash above the limit for declaration. That makes a "random" check unlikely on your way east from Germany to Poland, and from Poland to Germany you're going towards your duty station.

If you know your PESEL number the cops can verify you're a Polish citizen by calling the Polish Embassy/Consulate in Germany. Good Luck!