Organic Finish for Oak Hardwood Flooring

I live in a house built in 1948 and I pulled up the carpet the previous owner installed to find a huge patch with plywood and another smaller plywood patch. I used oak tongue and groove to do the small hole with a little design and used T&G oak on the large patch and it looks pretty good for an amateur. I have been sanding the rest of the flooring and want to keep the natural beauty of the oak grain and plan on using store bought polyurethane (water based) but wonder if I should go with something non toxic like linseed oil. Will this protect my floor from dirt etc and not dry out?

Here is the patch's and some more of the room sanded

Oops the large patch pic is when I was first starting to remove slats to lace in new slats. Gotta find them and post...

Ok here are better pics

Hi, Linseed oil might work. Depends upon who lives in the house and how scratched the floors will get.  This link will tell you about natural oil product and finish.  
https://www.heritagenaturalfinishes.com/SearchResults.asp?Cat=18

Interesting….unfortunately I don't have the luxury of being able to not walk on the floor for a month…would be two months for me since I can only do half of the floor at a time because I can't get the sofa out of the room, the door ways are too narrow but the front door is big enough, but I'm not leaving fabric furniture outside because of rodents and cats and whatever other creatures will poop and pee on it. So I'm going to use the polyurethane for now. My next place for sure will get the linseed oil and l'll put down some throw rugs to prevent Doobie, my little dog, from scratching it.
Thank you for the info!

I'm finishing up the hand sanding that the floor sander didn't get..it beat the crap out of me cause the machine weighs more than my 100 pounds

I love Chris's blog, and this wood finish sounds really nice - they also sell this finish pre-made, but batches sell out fast.

Lost Art Press - Make your own linseed/beewax wood finish

Awesome thank you for this recipe. Just will need to figure out how much I'll need on my next place.