Marilyn,
You do not want to remove the oscillating hook unless there is just no other way. If you do you will have to re-time the machine.
The feed dogs are held in with one screw passing through the shaft it's mounted to from the right to the left as you sit in front of the machine. Taking that out won't cause any problems. If the feed dogs won't come out, double check to make sure you removed the correct screw.
The bobbin carrier will come out when you lift up and pivot the bobbin carrier latch. They are sometimes a pain in the behind to get out, but they will come out.
The screw in the middle of the bobbin lifter only holds the springy tab on. The bobbin latch is mounted to the machine with a long pin locked down by a set screw from underneath. Put the screw back in.
You may have to resort to some stronger chemicals than just plain kerosene. I use Hoppe's #9 gun cleaning solvent and various brushes. It is mostly kerosene but with enough other chemicals to make it work very well on sewing machines. And if you get some on the surface it won't hurt if you wipe it off quickly.
Joe