Stain over danish oil. If the oil finish was a mineral oil commonly used for butcher block tops for example that oil will not harden. You should be able to apply stain to it. The wood was just drinking in the oil. It is okay to mix danish oil with stain provided that it is oil based and the wood including pine treated with the oil has had at least 48 hours to dry.
I could not get it to stay on the surface of the wood no matter how many coats i applied it just sank right in. Danish oil is simply extra thin wiping varnish with a little more oil and a churched up name. Danish oil markets a lot better on a label than thin wiping varnish with extra oil possibly with a pigment andor some dye. This was a mess.
After using two containers of oil i finally called it a night. Note here that an oil finish doesnt build in the conventional sense instead its the application process itself that makes most of the difference. Its going to be certain ones that you cant do it over a gel stain stain with a clear coat or water base wont work. Danish oil will penetrate the wood including pine through the stain however the wet appearance characteristic of the oil will not come through.
But even so one coat of oil finish is not that much of a finish. Oil based stains do somewhat close up the surface much as a layer of finishing oil does but in general theyre not recommended to be used when doing an oil finish.