I know that we cannot re-use Priority mail boxes for our books, unless we want to pay pay Priority prices. 

But what about a DHL bag?  I have one that is grey bubble-wrap on the outside  and has DHL stickers on the inside.   (I know, it seems backwards, but that's what it looks like.)  Is that ok to re-use?

The PO doesnt mind if it is wrapping from the competion, they just dont allow anyone re-using their own packaging. I have re-used FedEx stuff, and it was fine. Just make sure to mark through anything that even remotely resembles a bar code or address. Some folks even go so far as to take new DHL and FedEx mailers out of their boxes and use them. Seems like stealing to me. But as far as the USPS, using the competions' wrapping is fine.

Now that DHL is basically defunct, I plan on using lots of their packing material.

What the USPS objects to is competitor's logos appearing on the outside of USPS mail.  If you turn the DHL bag inside out you should be OK.  I looked and I can not find anything in the regulations which says users can not put whatever logo they want on the outside of their mail.

I dont think the USPS will object for you use the competitors packaging

as long as you have place postage on it

the post office will delivery it

they only object is when you try to use the POSTAL priority or express mails and try to send it first class or media mail

then they WILL OBJECT and if caught charge the recipient the current priority or express mail rates

Ditto what Mark said. 

You can have almost anything on the outside of your box/envelope.