Is it safe to stain some small wood pieces with Danish oil in my basement?
Oil finishes have been used on wood in homes for years, I have done several hard wood floors with this same brand it drys fairly quickly but you should make sure to have adequate fresh air for several hours, a couple of boards may not be much but some folks are very sensitive to the odors. Make sure to follow the mfg instructions and by following  them the product is safe to use.