Please attach a photo ... I can't visualize "grain running in opposite directions" because it really has to run the long way on the strips.

Why would a washroom have been in the front hall? Was the house chopped up and you are "un-chopping it?

The texture - may have never been finished, may have been damaged or badly cared for.

sqsemi, You can't attach photos, you'll have to upload them from your computer or from flicker, photobucket or some other on line photo site.

Sorry for the delay...
Here is a picture of the floor. What I mean by grain running in different direction, is that on one board it runs from top to bottom of room. The next board runs from bottom to top of room . I think! I think this because if I run my hand over the board I get slivers in one direction and not the other.
The washroom in the front hall was a vestige of either the previous duplexing of the house or maybe it's previous incarnation as a boarding house.
It may never have been sanded... but is definitely well waxed (which is near impossible to get off!).

Oh shoot, I realize that the photo may be confusing. I am NOT talking about the boards in the foreground, which are perpendicular to form a border. I mean the other boards - can you see the alternating grain patterns on those?

That floor is heavily worn, perhaps worn out. It will be dangerous for bare feet and will snag socks the way it is. If it's too thin to withstand a sanding IDK if you have many alternatives. The 7th, 9th, 14th and 17th boards look particularly well-scoured and need maybe 1/8" taken off before they will be smooth. If they are not T&G it should be a simple matter to replace them individually.
Casey

That's a surprising thought, Casey. These floorboards have been covered almost their entire life! Are you sure they have just never been sanded?
They are quite thick (3/8") and NOT T+G, so I could sand, but I kind of like the texture. We walk around in socks all the time (almost 3 years) and these floors never splinter - unlike those that have been previously sanded and the polyurethane is thin.
I'm confused.
In any event, is it reasonable to think that the grain may run in opposite direction every other board?

OK, on my screen they look very heavily worn, but you see them IRL.
Pic is not of high enough resolution to see the runout effect you're describing.
Casey

What you see as "grain running in the opposite direction" I see as boards with raised grain. Sometimes this is a result of damage over time, possibly from moisture. It could also be that some of the boards were from different trees with different characteristics as far as hardness (some exposed growth rings may be softer and got more eroded). Lastly, when oak is sawn it will reveal different grain patterns depending on whether individual boards were plain sawn, radially sawn, or quarter sawn. Typically these will all be present in bundles of oak flooring. I can't tell absolutely what is responsible for the somewhat irregular appearance, but I think that, if it is professionally sanded and stained, the floor will look pretty uniform.