Your walls will need some deglossing to help the primer stick and provide a good foundation for the top coat of paint. Each method you mentioned will work by themselves.
1) The easiest is washing with TSP. This cleaner will degloss most surfaces including oil based paint. If the paint is very hard, TSP won't do much in the form of deglossing. It is still worth trying.
For washing the walls of an entire room, use a sponge mop. This will drastically speed up the washing. Make sure to rince well with fresh water.
2) Sanding is a very good option. This will degloss and roughen the surface. Sanding works best on smooth walls, no texture. Use 150 grit sanding paper and a pole sander. This is the same hand sander used by drywallers when finishing walls and ceilings. You can find this tool at hardware stores and it is very inexpensive.
3) A liquid deglosser will work, but is a very labor intensive way of prepping your walls.
Washing with TSP and sanding are the best ways to prepare your walls. Plus, they can be combined for the best results.
I would test an area with a strong TSP solution and see what happens. If the surface is visibly affected, less gloss, then this will be a good way to degloss. If your walls aren't affected, then sanding is the next method to try. Save using a liquid deglosser as a last resort.
After the deglossing comes priming. Use a fast drying oil based primer. Two good primers are Kilz Original Oil Base and Zinsser Cover Stain. Both will stick very well and dry fast. Any good universal oil based primer will work.
Allow the primer to dry for 2-3 hours before painting, even though the can says only wait for one hour. The extra time drying will help it cure before it is covered with paint.