If you get air in the blood (like .1 of a cc) that won't kill you. Takes more then that. The body would absorb that. Now if oil gets in there...well there's your stroke. Ha
Actually, It depends on how much they inject, and where they inject it. While I wasn't able to find any studies of this exact case, there have been cases where bodybuilders have injected steroids in an oil solution as well as a young woman who injected peppermint oil.
In these cases the patients developed difficulty breathing and presented very similarly to patients experiencing a severe Pulmonary Embolus.