I feel like I'm going crazy so I thought if I shared it with people maybe I could get some questions answered.
I moved into our new home in September 2011. It is a old home built in the early 1900.

Anywhere I go in the house I feel like I have someone with me, always being watched. The lights sometime fade and I have always put it down to an electrical issue or loadshedding as we have had so much of that. Since we have moved into the house, I have been having bad dreams, dreams about a woman. I always feel like I am very awake, like I am walking around my house yet I wake up in bed. The woman is screaming and always comes across in a very threating way.
Last night (This has never happened before) I felt very cold hands grapping my fingers, I thought it was my son but when I woke up and chacked on him he was fast asleep.
Could there really be something happening and if so, how do I know what it is and what they want from me?

You're not crazy. Obviously a house that old can have some history to it, and possibly that which involved the lady you dream about. This is, however, not the spirit of the lady you are dreaming about, but a spirit mimicking her and whatever it is that happened there. Boiled down, the spirit simply wants to be an influence in your life... whether it leads to you seeking out dark spiritual matters or if it simply becomes an annoyance and confusion in your life. It's intentions are not good and are deceptive at BEST. The bible can give you quite a bit of detail as to what this thing really is... moreso than people really know.

I have spoken to my pastor, he advised that when she is there you should pray and if it gets worse put oils on the doors, do you think this will work?

No, I do not think that will work. I know your pastor's intentions are nothing but good, but he needs to re-examine how the bible shows us to deal with these spirits. May I ask what denomination you attend? Prayer may or may not help... in that I mean if it gets bad, prayer might subside the manifestation but it will not remove it in MOST cases. Has your pastor dealt with these situations before?