I see two potential problems, apart from the noxious fumes which should, in theory, not occur if your burner is properly sealed.
1. You may create noticeable smoke which could land you in trouble if someone complains (unless you have the benefit of not being in a smokeless zone, of course).
2. Even if you have a chimney liner, burning wood such as you have listed could, eventually, lead to a chimney fire.
Using other than properly seasoned or kiln-dried wood just to light your fire (eg, softwood kindling, paper, cardboard) is OK, but burning such things routinely is not to be advised.