My .02 cents...
Any clear top coat on birch (shellac, oil/water based polyurethane, etc.) will give the natural blonde look. Danish oil is actually a thinned wiping varnish and not a true oil, but would give the desired effect. Tung oil is sold both as a true oil and a wiping varnish and would also be suitable. Polyurethane will hold up to more abuse than shellac and is sold in gloss, semi gloss, and satin to suit whatever sheen you would like.
For the orange, well, orange shellac springs to mind first. Boiled linseed oil gives a somewhat orange cast, especially after several applications. Also I've used a stain called Colonial Maple by Minwax that gave an orange color to wood. Any of these options also allow for being top coated with polyurethane.
Hope this is helpful.