Hi Old
No you can’t put Pre-catalyst or Acid Catalyst lacquers over varnish they are both cellulose based and therefore act as a paint striper. And just by the name alone danish oil is a oil then I would think it would be very unlikely that varnish would take to the Danish oil.
You ask if you need something more robust and I would say as a stairs is a high traffic are then the answer is yes and that’s when a pre-catalyst or Acid Catalyst lacquer comes into its own very, very robust it is what is used thought the furniture trade and shop fitters.
Oil based varnish will turn a yellow colour in a very short space of time and you can’t do any thing about that know as you have already used it. Catalyst lacquers stop all most clear they are known as colour fast. Catalyst lacquer give a finish that you see on M & S furniture etc not the thick plastic look of oil based varnish.
You can knock the gloss off varnish and make it look less plastic by using 320 or 500grit silicon carbide paper and white sprite using the white spirit as the lubricate as you us would water with wet & dry. Using the silicon carbide paper on a sanding block you will remove all the brush marks leaving the surface smooth and flat but in a mat finish. Then apply a good quality wax and buff to the required sheen. Or apply a single coat of danish oil but I would go with the wax.