Yea, actually Ive done this before so I'm sort of an expert
I did this with my old dell computer, and it was getting old and dusty so i decided to submerge it in oil. You can check it out in my sig. I also have a build log of it too.
The pros of doing this is that it will preserve the life of your computer for a very long time, as the oil helps keep all the metals from corroding. Mineral oil is a natural preservative. And, if done right, it does cool the computer rather well.
There are many cons to doing this though, as you will never probably upgrade, as it is a pain to remove the oil from the components, and it can make a mess as the oil has a tendency to wick up the cables, causing oil to form all around the table. It gets kind of disgusting. The simple way to fix this is to just make sure your cables don't touch the oil, just make sure the connections are made outside the oil so you wont have a mess. Also, if you have a small tank (thats what I got), you will have less amount of oil, thus you will need a radiator + pump to cool the oil.
I currently run my oil PC passively cooled. It runs fine as the oil takes a rather long time to heat up, but I can't play games for too long as the oil begins to get really hot, and I'm worried the glass might crack.
SO if you plan to do this, be ready to never upgrade or change any of the components in the computer as the oil will get into everything and its disgusting, and also get ready to get a simple loop to cool down the oil if you are planning to use a tiny fish tank. However, you will get the added benefit of silence, as all the fans will be submerged and make no noise, (the only thing you cant put in oil is the HDD as it has moving parts, and the oil might screw that up), only the HDD will make noise, as well as a very long lasting PC.