Hi all,
Upon more research, I think I might be wrong about these being mahogany. The grain on walnut is much tighter--it looks closer to freek's earlier pictures.
@FreekYou can use paint stripper and a soft brass brush to try to get as much of the paint out of the grain. If you are oiling, I recommend using something like Watco Danish Oil in either medium or dark walnut.
After stripping again, I would sand from 120 to 180 grit, vacuum off all dust then clean with mineral spirits. Let dry 30-60 minutes, then apply the oil with 180 grit sandpaper for the first coat, let sit for 20-30 minutes, then wipe dry. Next day, if you still have grain to fill, apply the second coat of oil, apply with 220 grit sandpaper, wipe dry after 15-20 minutes. If you are happy with the grain after the first application, simply apply the second coat of oil with a cloth, then wipe dry after 15-20 minutes. Let oil dry for 24-48 hours. Longer is better, usually.
The 220 grit can serve as you final sanding. You can go to 320 grit for the second application of oil if you want a smoother finish. After 2-3 days, apply a quality wax, then buff out. I am a fan of Howard's Feed-n-Wax. It is easy to apply, and it is easy to reapply after 12-16 months. One or two coats should suffice.
BTW, when you sand the veneer without oil, collect the sanding dust you generate in a small jar. If you ever have to touch up walnut, you can mix the dust with your oil to fill defects.
Peter