|No, this is as fine a place as any to ask how to research your family tree.|
It sounds like the only name you are sure of is your father, and if he was born after 1940, then it will be tougher to research this than if he was born before April 1 1940.
Take a look at your birth certificate, it may give your father's age at that time.
Yes, privacy issues will make it more difficult until you can find your father's family to go backwards with, but it can be done.
If your dad was born before the 1940 census, then once it is indexed, you can hunt for him in that, and it will answer a whole lot of questions. But that is a ways off - images are browse only now, you need an address. But if you know where your dad's family was likely to have been in 1940, you certainly could try seeing who is at that address. If it is Pikes, even if your dad was not born yet, then you will be in luck.
If you think Leo Pike was his father, then go ahead and search the 1920 and 1930 censuses for all Leo* Pikes you can find and consider all of them possible family until facts turn up enabling you to rule them out.
This should get you started. I have a bunch of pages with information about finding out more about your ancestors and links to various free resources, including census records. I think the best starting place may be the following. From there, you can jump to the free resources page from the left or top menu (I forget which) as well as when the resources page is linked from various sections.