I'm sorry to hear of your trouble, perhaps I can help.
There are almost no oil/varnish finishes out there that are durable enough for floor work. But here are two : http://www.triedandtruewoodfinish.com and http://www.waterlox.com. The tried and true true oil/ varnish is really meant for furniture, but is truly non toxic. And the Waterlox brand have finishes that are more like varnishes than oils, but are suitable for floors. You should not use a pure oil finish on a floor, as it will have no water resistance. These oil/varnish blends are the best of both worlds, but are difficult and expensive to apply, so would cost a lot more than a regular oil modified polyurethane finish. They have the advantage of easy touch ups, but any dent or scratch will still show through. They should not be waxed as is often the suggestion. You will be defeating the purpose of the touch-up-ability of these finishes. Once the wax is applied (any floor finish has to cure for at least 1 month) you can only touch up with wax, not the floor finish any more.
For all of my floors I only use oil modified polyurethane. It has a fairly quick dry time. I apply one thin coat and by the next afternoon it is dry enough to be scuffed, and the second coat brushed on. I skip a day and scuff again and apply the third coat. It's ready for moderate use in 48 hours, and cures in one month. The finish will get harder over the years, and should last 10-20 years in light use areas. It's easy to re-coat, but cannot be repaired invisibly, any touch up coat really show, unless you do the whole board or wall to wall.
Compare that to the oil/ varnishes. You will need to apply at least 5-6 coats of a true oil/varnish. This will take all together about 2 weeks to complete. Let each coat dry enough to be steel wooled (two days each coat). Don't be fooled by the fast dry times of some company's instructions, they say that the OMP (oil mdofied polyurethane) that I use dries in 4 hours, it's simply not true. And the oil/ varnish finish will not be as scuff resistant or as durable as the OMP.
You will find yourself recoating an oil/varnish floor every 2-4 years to keep it looking good, and only of you use the Tried And True finishes will you have a real non-toxic finish (no heavy metallic dryers), and this will cost you a bundle over the years. With the waterlox brand I'm afraid you will be exposing yourself to lots of toxic fumes as you touch up and re-coat these floor so often.
Oh, and since you say you have a white or pale stained floor, you really shouldn't be using a oil based finish in any case. It will darken quite a bit in just a few years. Better to use a clear water based finish like Street Shoe (http://www.basiccoatings.com) or Traffic (http://www.bonakemi.com).
As always your Most humble servant, Joseph, the Wood Floor Doctor.