First, FORGET about oil! Decades ago and earlier, fans were constructed so you actually could disassemble them to reach the bearings and add a tiny drop of light oil, then re-assemble to work. NOT SO for a long time now. The fan interior design is now quite different, and they all are built with sealed-up frames. You cannot break the frame open to get inside to components, and you cannot re-assemble the cracked mess if you try! If you simply spray or drip oil onto the exterior of the fan, that oil will go everywhere and cause more problems inside by contaminating all the wrong things. When fan bearings wear out now, your only choice is to replace the fan.
Now, we need a clearer description of your issue. Almost all the replies above assume you have an older fan with worn out bearings, and that may NOT be your issue. IF your bearings are worn, there is a common sequence of developing symptoms. First you notice that the fan makes an odd noise when it first starts up from being cold and off for a long time. But after a minute or less the noise stops and does not happen again. If you reboot it is not there. But if you shut down for hours so the system cools off, the noise IS there again for a short time. As months go by, the period of initial noise gets longer. Eventually the noise becomes permanent. And after that, it stops completely because the fan is seized up and NOT working at all! So, IF that is your pattern, plan to replace the fan before it is giving almost constant noise.
There's another cause that many have seen that has nothing to do with worn fan bearings or old fans. There are two very similar cooling control systems in your computer. One is only for cooling your CPU chip, and the other is concerned with cooling the entire case interior and the mobo components. Each system uses a temperature sensor to guide how fast its fans run to blow cooling air. Many such systems change the fan speed the control in steps, not in a smooth continuous manner. When this happens (either speed up or slow down) the user may notice the sound change. SOMETIMES this becomes annoying because it happens frequently. Usually that is because, just by coincidence, the actual normal operating temperature at the related sensor is very close to the point of the control system where it is programmed to change speeds in one fair-sized step. So, as the small normal variations of temperature happen, they become very obvious repeated changes of fan noise up and down. This is NOT a flaw of the parts and does not require replacing anything. If you do not want simply to ignore it, there is a simple fix you can do by adjusting the settings of the automatic fan control system for whichever fan is doing all the speed changing.
So, IF your symptoms are NOT like the development of worn fan bearings, and more like the second cause I described above, post back here for details of how to adjust. For that we need to know what computer system - maker and model - you have. OR, if it was custom-built from components, tell us the maker and model of the motherboard, and what CPU cooler system you have. We also will need to help you figure out whether this noise comes from the CPU cooler or the case ventilation fans. With such info we can look up details and give you more complete instructions.
On the other hand, if your issue really does appear to be part way along the developing sequence of fan bearing wear, we do need to identify which fan is making the noise. IF it is the CPU cooler system, we need to know exactly what cooler unit is mounted on the CPU chip. In many such cases one can replace ONLY the fan of that unit, and not remove and replace the entire cooler on top of the CPU. We can advise with more info from you.
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