I know of at least one other person with this problem.

I have a '97 Cutlass Supreme. The coolant resivior is full of gunk. The coolant looks and smells oily. I tried to clean it out as best I could, but it didn't help much. I'm thinking about buying a new coolant tank. Does this happen to anyone else?

My best suggestion would be remove the tank and clean it out and flush the radiator. You can get a radiator flush bottle that explains how to do it that the easiest but doesn't flush as good as my prefured method, which is to get a radiator flush kit, which you cut the heater hose and install an adaptor to hook a garden hose to. It is as difficult as it sounds, and it stay there incase you need to do it again in the future, it also comes with instuctions. Just remember to properly discard the old antifreeze in both methods, and use new antifreeze of the same color. If it has green use green, if it has red or orange use that color. If you change color it can cause big problems in the future. AND KEEP ALL ANTIFREEZE AWAY FROM PETS, THEY LIKE TO DRINK IT, BUT IT WILL KILL THEM. And never flush if the engine is hot.

Yes they do get clogged.

Remove the reservoir. You will see a brass tube going into the plastic reservoir.
Remove the brass tube, it will come right out. This will give you a bigger hole to blow out the goop with. Hold the reservoir upside down and put the garden hose on the end - that usually does the trick.

Check by making sure a clear stream flows out when you stick the garden hose in the top of the reservoir.

Then reinstall it.

Before hooking up the hose … I also flush the hose from the radiator. Remove the cap and clean any visible silicone from around the filler neck.

Oil in the coolant??? hope there's no coolant in the oil. If you also notice your oil level is low, you may have a lower intake gasket leak. Seems to be a common issue. My '95 had the same problem. I was lucky I never had coolant in the oil. Keep a close eye out for coolant in the oil (foamy brown). It'll burn up an engine quick.