Can NCOs give you a lawful order about a non-military related matter?

I'd make an appointment with your JAG. I'd also keep your mouth shut until you talk to them.

If you are the one under investigation, the only thing you should say to the civilian police is: I invoke my 4th, 5th, and 6th Amendment rights."
The only thing you should say to any military member, whether your supervisor, MPs, CID, Cdr, is: "I invoke my 5th Amendment and Article 31 right to remain silent "
Then, you should seek legal counsel. JAG for the issue of refusing to talk about the matter with your supervisor, and the matter at issue with the civilian law enforcement. (JAG won't represent you with civilian authorities. )
A defense attorney, or public defender, regarding the matter at issue with the civilian authorities.
After you've spoken with JAG and/or a defense attorney, don't speak to ANYONE about the matter, and refer questions to them.
Your supervisor erred if she failed to advise you of your rights.

Practice saying this phrase: "I plead the 5th to any question you ask. I also invoke my right to have an attorney present." NEVER TALK TO THE POLICE/DETECTIVE/CID/NCIS/OSI/FBI/ETC WITHOUT HAVING LEGAL COUNSEL PRESENT!!! EVER!! And this is coming from a former police officer (both military and civilian).

Now that being said, yes, your CoC can order you to respond to an investigative authority. What they CAN NOT do is force you to give incriminating statements without the benefit of legal counsel present. My suggestion would be to tactfully inform your NCO and/or Officer that you will be happy to speak with an investigator just as soon as you can retain the services of a qualified attorney. And for Pete's Sake, if your lawyer tells you to shut your mouth, DO EXACTLY THAT!!