You could try using paint-stripper or varnish-stripper to remove what is possibly a dark varnish. Test a small area in the least visible spot before committing. Alternatively use a fine sand paper to rub back to the natural wood. Again, try sanding a small area somewhere less visible if possible. Oak is very desirable and so even if cost was not an issue I wouldn’t recommend ripping it out – try to keep the panelling as a feature.

If you are able to sand or strip as described above and the exposed wood is lighter, once you have done all of the panelling you will need to varnish it afresh. This time use a clear or neutral varnish to preserve the wood without staining it a dark colour.

As for the crumbling artex, I recommend removing and re-plastering. Get two or three plasterers to give you a quote. Ask them to give you a price for removing the existing plaster and re-plastering separately. If your budget is tight you can save by removing the old plaster yourself. Take care not to damage the surrounding walls, wear safety goggles and a hard hat to protect yourself, and lay down dust sheets to catch the falling plaster as you go.