Overflow resevior for the radiator.

have a compression test done as that will most likely be a blown head gasket or cracked head allowing combustion pressure into the cooling system. A quick check is to remove the radiator cap and fill right to the top . Run the engine and if you see small bubbles in the water or it tends to belch out then it will be the gasket of cracked.

The oil in the reservoir tank ( radiator ) may be from a cracked transmission oil cooler in the radiator. Have it pressure tested

I suspect a crack in the head or block. The cooling system is suppose to be closed so any air has to be coming from somewhere - if the head gasket is good then the air is likely to be coming from a crack. A pressure test will confirm if your system is not air tight. That is if you are seeing bubbles in the radiator water if you just mean you are losing water through the overflow then it might just be the radiator cap needs replacing as it is not sealing the system when it gets hot.

If you are sure there are no leaks, you could have air in the cooling system and it is slowly bleeding off. Which would require you to refill the tank.
Leaks could include a head gasket which would allow coolant to be burned out the exhaust pipe and not be visible.

Sounds like you need to disconnect the Radiators' electric fans and have them tested. You absolutely must have them working, or your car will overheat. Check to see if the Temperature guage is working.

You need to go to a good autoparts store and have them test the fans and charge and test your battery. You may need some sensors to activate the Radiator fans, but you could be running the battery down with shorted cooling fans.

There are also Relays which work with the Radiator fans. The overflow will stabilize once the water gets into where it belongs. Make sure your Thermostat is not clogged with the sealer.

There will be one hose that goes from the radiator to the resivor, then one that goes from the resivor, which is an overflow tube, it does not connect to anything.

It has to be a gasket related problem or radiator. Check your oil cooler lines, they maybe allowing oil to get into radiator, therefore prob bad radiator but sounds like intake or worse yet Head gasket problem.

It sounds like your heater hoses have a blockage. Replace them and it should clear up the problem.
Some models eliminated the radiator cap and can only be filled through the overflow resevior.

Your overflow tank works on suction to return coolant to the radiator. Check the line and nipple ends for any cracking (cracking on the plastic radiator nippl is very commom). The radiator nipple is not under high prrssure like the fluid under the cap (inside the coolant system). It's on the otherside of the cap and will never "stream or gush" coolant (uless you are over heating badly). As the coolant in the radiator cools it creates a vacuum and draws coolant back from the overflow throgh a small hose. You might not see any leaks as coolant heats up and travels to the overflow. It might be a very small leak and you are usaully driving around and drying up before you see it. Even with a very small crack it will only draw in air and not liquid (as liquid is way heavier than air). Also, I've seen where people have taken out (or fallen out) the tube attached to the overflow cap that goes down deep into the overflow tank. That tube should be long enough to almost reach the bottom of the tank. It's hard to know if something is missing if you do not know it was suppose to be there in th first place but it needs to be there.

I had the same problem and it was due to a tiny tiny crack in my resevior. my radiator was full too. I had a new resevior installed and now everything is perfect.