I have oak cabinets and worked with them as they are - though I did refinish them but kept them close to the same color. Pictures are in my "my pics" idea book in case there is something you see that is helpful. I know it is difficult to find pictures with oak cabinets right now. My trim is white. I painted my 70's dark stained pine many years ago. My style is a sort of Victorian cottage / French Country style: http://www.houzz.com/ideabooks/57579129/thumbs/my-pics-work-in-progress

blue is perfect for oak. did you see all the colors I posted in my other comment? I put a few blues in there. this blue would look really nice w/the oak I also like the greens. Sage greens look great w/oak and will work w/your green frame. This is Silver Sage SW Svelte Sage Behr,,Quiet Moments bring home some other samples (if you use Behr, you can get the $2 samples. BM is at $7 each. )' these are some gray/greens and would look nice. I don't like the blue/grays w/the oak because those paints tend to run on the 'cool' side, whereas oak is warmer. Pale Oak (BM) may be nice for the other rooms. maybe try this link for the best wall colors w/oak cabinets https://www.hometalk.com/2389914/5-top-wall-colors-for-kitchens-with-oak-cabinets this one is Pleasant Valley

The cheap way: Remove carpet, add a decorative TRIM at the doorways (where the two woods meet) and lay the new wood PERPENDICULAR to the hardwood in the rest of the home. Sand and refinish all. The most APPROPRIATE way (to lay the new wood parallel to existing): Remove old wood floor, lay new plywood subfloor and lay new wood flooring parallel (in the same direction) as the existing hardwood. Sand and refinish all. You will need to choose between FINANCIAL vs. Aesthetic concerns. I'm someone who appreciates the TECHNICAL side of the building industry (aka. Best Practices) who is also a cheap/lazy person who pays attention to finances MUCH more than I pay attention to aesthetics. I choose the 'decorative trim' with the new wood running perpendicular to the existing wood. It is inside the budget AND it gets you the 'right' type of install (which you have already been told is best) AND it gets a solid hardwood throughout the house. Done. Done. And done. There is ONE option that NO ONE has discussed with you: Remove ALL flooring surfaces and install ONE wood floor. Sand and refinish.

I have just had my walls painted. Now going to do the flooring. So glad I waited to do the flooring. The painting and new blinds make the rooms look so much brighter. Previously considered the Calypso oak before the painting and was hesitant. Does it have a warmer golden or honey cast to it. Pictures don't seem to be accurate. I need a lighter color don't want anything that is dark and going to show the dust etc. Some of the lighter colors looked washed out. Don't want a golden color either but would prefer it be a warmer look. Do you like the Calypso oak and is it easy to clean.