Should oil be going into radiator of a 1998 Chevy Blazer

Engine Oil should not be going into the radiator of ANY vehicle, including your 1998 Blazer. Radiator is for coolant ONLY. If there is oil in there, take it to your mechanic ASAP.

Do you mean seperate oil lines into the rad. The 1/2 ton and larger trucks had engine oil cooling lines running from above the oil filter to the rad (driverside of the rad). Usually on z-71's or truck with tow packages. Your Blazer may have this system. If it's an automatic the tranny cooling lines would connect to the opposite side of the rad. For these two systems the oil(s) run through coils in the sides of the rad and are imersed in the engine coolant. They are and must remain separate from the coolant.

Engine oil or trans fluid? Either way it's not good the transmission cooler is internal to the radiator and a full flush of the radiator and transmission along with new filter is required after replacing the radiator

i had tans fluid fill up the radiator resivore tank on my 2001 chevy blazer LT but don't show no signs of any fluid coming from radiator into transmission i even put another quart in trans after and the drove around and then started running out radiator resevore overflow but still showing no sighs of radiator fluid entering transmission . ????? but im sure in bad radiator ,,going to start there... hope im not wrong

Mark - replace the radiator.