Cut back the oleander branches until its main branch cluster is easily accessible and you are able to dig around it without too much trouble.
Dig out the area around the main branch cluster. This will reveal several large roots, as well as the main root crown. You will need to dig out the root crown in order to fully remove the oleander.
Use your heavy cutting implement to cut through the oleander roots. Depending on the size of the plant, these roots could be as large as your arm, or even larger.
Continue digging around the root crown --- cutting through the roots as you go --- until you are able to pull the crown free of the dirt.