Can hydrocarbons undergo combustion without oxygen present?
They would certainly combust if meeting a worse adversary than oxygen. $\ce{ClF3}$ would oxidize them, with extreme certainty, rapidity and violence.

Here is a short excerpt from the Wikipedia article of $\ce{ClF3}$ which amused me:


  It is, of course, extremely toxic, but that's the least of the
  problem. It is hypergolic with every known fuel, and so rapidly
  hypergolic that no ignition delay has ever been measured. It is also
  hypergolic with such things as cloth, wood, and test engineers, not to
  mention asbestos, sand, and water — with which it reacts explosively.
  It can be kept in some of the ordinary structural metals — steel,
  copper, aluminum, etc. — because of the formation of a thin film of
  insoluble metal fluoride which protects the bulk of the metal, just as
  the invisible coat of oxide on aluminum keeps it from burning up in
  the atmosphere. If, however, this coat is melted or scrubbed off, and
  has no chance to reform, the operator is confronted with the problem
  of coping with a metal-fluorine fire. For dealing with this situation,
  I have always recommended a good pair of running shoes.