|Absolutely do not burn it if you suspect that any of it may be Poison Ivy, Oak, or Sumac. The Urishoil which causes the allergic reaction remains active for a very longtime - even years after being cut down. If the smoke is inhaled by anyone this does damage lung tissue and can lead to a long hospital visit or death.
The best thing to do is cover yourself head to toe and wear heavy rubber gloves, bag the plants, roots and debris in plastic, then take to the dumpster or land fill. Make sure to dispose of the gloves, wash your clothes right away. If you think you may have come in skin contact with it you can use Tecnu wash and shower in cold water.
Hope this helps!