Beautiful machine! :) I would try PB Blaster or Kroil.
I've tried Liquid Wrench and it's okay, but in my limited experience, PB Blaster is much faster.
As for oil, I've been so happy with TriFlow that I don't usually use anything else on my machines, lately. Regular sewing machine oil is fine and it doesn't matter what brand. But, TriFlow is really wonderful stuff - most of it evaporates away and it leaves "Teflon" behind as a semi-dry lubricant. Over time, it dislodges old gunky oil and makes it easy to wipe away. Jenny at sew-classic.com has it - a 2oz bottle lasts a very long time. She's also got the grease for gears if you need it.
Good luck with your machine - hope she loosens up and starts doing what she was made to do - she's certainly decorative! :)