When you use oil try one or two drops in one of your palms and rub them together and then gently slide the ends of your hair through your palms.  Any extra you feel on your hands can be applied to the length(from the ears down).  You had probably used too much oil the time that you tried it.  When you start out with a drop or two you haven't applied too much and your hair most likely will not be greasy.
Oiling and conditioning are two different things.  After you shampoo, apply conditioner from the ears down.  If you need to apply it to the whole head do so sparingly on the top.  Conditioning reduces tangles and helps the hair relax.
Oiling your hair adds and retains moisture.
HTH  

usually less is more with oil I think, but I prefer to use the pre-measured hot oil treatments u can buy at drugstores. sometimes u can find the ones that heat up just from the heat of your shower.

Shea butter can be wonderful for hair.  It seems to work best on curly types.  I use it on my skin frequently and love how soft my skin will be.  But it is a bit too much for my fine hair - it tends to leave my hair greasy.