I think I would continue the oak from the great room into at least the dining room.

I would oak everywhere.

Why is "now 14 years old" relevant? Are you suggesting it's too old to keep?

The same as the other wood floor

I prefer the look and feel for wood from living room through kitchen and dining. However, if this is in a warm climate, all tile (although you didn't mention wanting to remove oak flooring) also looks nice and is functional. It really depends on the style of your house and the look you want to achieve.

You will need to decide what it is you want for a floor in the kitchen. Do you want hardwood or do you want tile? If you want tile, then go ahead and replace the tile in the kitchen with a stone/tile looking product.

Then you will decide if you want your dining room to be part of the KITCHEN (match the flooring as you have it now) or part of the living room (which means you match the oak hardwood).

I would NOT put engineered hardwood up against solid hardwood. It rarely works out well. Either pull the solid oak INTO the dining room (sand and refinish ALL hardwood at the same time) or put the new kitchen tile into the dining room (just as you have it now). Please do NOT add a third floor inside so short a distance.

We have installed engineered wood floor (santos mahogany) right up to our hardwood santos in two locations in our house. Weather or not this is a good idea has to do with the environment your floor is subjected to. Engineered and hardwood materials will expand very differently depending on variations in temperature and moisture at your installation site. There are reasons for installing both and sometimes you can install them next to each other without problems....but you need to speak to a professional and be sure it is warrantied if you do proceed down this path.