Is it best to put oil on the inner or outer of the chain?
If you think about it, the purpose of oiling is to lubricate where you have metal moving against metal.

So in the diagram below:



you need to oil the pin/roller area. There's no point oiling the face plates (which I think is what you're saying?).

When you oil, know how many links are in the chain (or mark your start link), and go around the whole chain once, oiling each roller. That's all you need to do. No need to do quarter turns or repeat three times.

Then, when you've done, wipe off the excess oil with something dry. A bit of rag or kitchen towel will do.