I would remove all the tile, or else you will have a bad transition between the tile, and the wood. Would stay with the oak, you could always paint the kitchen cabinets white if you don't want the matchy matchy look, or stain them darker.

The transition from wood to tile in the hallway looks good. Don't worry about transitions.

It looks like the oak floor in your living room is classic and in good condition. Your kitchen cabs also look to be in fine shape. I think you will be happy with oak floors the same color as the living room. You can have the lr floors refinished to match the new floor if you like.

I, too, have oak floors and cabinets in my kitchen. They look great
together! The floors are very low maintenance and very easy on legs and feet. You'll be delighted with your new floors!

Thanks sloyd and Sherman
Well you make me feel better since you have both oak cabinets and floors.
I guess I will go ahead with an oak floor.
I plan on a beigy tan rectangular tile for entrane, maybe about a 7 by 14 tile.
Anyone else have suggestions.

I would suggest having the current floors sanded down to bare wood and then when the new wood is laid, you can finish them all to match. For the color, I would suggest something browner and darker than your cabinets, but not too dark. You want a difference in the colors so it's obvious that the cabinets are one color and the floors are another. It's fine that they are both oak, but if they are the same color, you lose any contrast that allows them to be viewed for their own special beauty and they blend into each other to form a blob of color that doesn't let you appreciate each individually.