Can paper burn without oxygen or air? If you put a paper inside an oven vacuum packed and go beyond 250ºC, will it burn? There's no oxidizer. If not, what will happen?
 A: This is really chemistry rather than physics. Paper is mainly made from cellulose, and when heated in a vacuum cellulose undergoes a process called pyrolysis. The mechanisms involved are enormously complicated. Have a look at this paper to get some idea of how many different reaction pathways are involved. The end result of pyrolysis tends to be graphite (i.e. charcoal!), so your paper would probably end up as a graphite sheet, though that would take temperatures considerably higher than 250ºC.
Googling for pyrolysis of cellulose or some similar term will find you lots more on the subject. It's of commercial interest for turning biomass into fuel.
A: It would not burn in the classical, combustion sense because as you noted, there is no oxygen present. Paper is a carbon-based material and so it requires oxygen to combust and form products like solid carbon, carbon dioxide, carbon monoxide, etc.. 
However, combustion is not the only thing that could happen here. In theory, if you heated it enough, you could add enough energy to the paper that the molecules begin to vibrate themselves loose from one another. And you could, in theory, add enough energy that they vibrate themselves apart and begin to decompose. And it's possible to add enough energy that electrons start popping off of them and the paper ionizes. 
None of which is burning, but it would result in chemical changes in the paper.
A: My guess is that if in theory you gave it enough heat, then the molecules of the paper would vibrate so much they would produce a gas first, then if some of the molecules were oxidant agents you might get a burn. Almost certainly though  depending on the paper material the molecules may be vibrating and moving so fast  and being pushed away from  each other they would be unable to combine so no burn.  Great question
A: The title poses, "Can paper burn without oxygen or air?"
 A little sneaky pedantry here from a chemist - 
No Oxygen present, no air either, nor any mention of a vacuum.
This allows us the presence of other strong oxidisers such as Chlorine and other halogens which will support combustion, which is what most people mean by "burn".
As an aside, I well remember a chemistry practical demonstration where my teacher plunged a spoon of Phosphorus into a cylinder of pure chlorine to see a pale green flame spontaneusly appear,  accompanied by copious white smoke (Phoshorus pentachloride) being emitted. 
So the answer is yes, but only in very uncommon enviroments, but which are found in the chemical industry where the Fire Service need to be aware of potential fire hazards.
