Are you open to painting the cabinets?

Some decluttering is needed. First thing you can do...at no cost...is take everything off the fridge. A soft white or cream for the walls would work with the cabinets. For me the green walls are are emphasizing the orange tone in the wood. Quartz for the counters would be nice...a light color with simple veining. I'm guessing new appliances aren't in the budget. Black ones can become "black holes." Stainless would be better with complimenting hardware on the cabinets. I would do a simple subway tile backsplash that works with the new counters, floor and paint.

Same question as bobsmith regarding painting cabs...?

I would start by looking at pics of refreshed oak kitchens or wood kitchens in general and see what stands out to you - makes you smile and reflects your style.

Some general thoughts - if you do a backsplash, it comes after the counters. Oak cabinets look best with a simple backsplash, and do not get a 4" splash made from your countertop material if you do plan on a backsplash. A good way to determine a backsplash color is to look at a light color in your countertop that also works well with your wood tone and do a simple tile splash in that color. Also, wait till the countertops are in to make a final backsplash decision. When I saw the "big picture" with my countertops in, I change up the color tone of my backsplash decision a bit. If you do a black or soapstone countertop, a light colored backsplash is still a good choice.

I do have oak hardwood in my oak kitchen. Some feel like that would be too much wood, but I have an L shaped kitchen so am not surrounded by wood cabinets. Many pics of wood kitchens have wood flooring. I have an oak kitchenette in my basement - darker tone - and a stone look tile with that. Sometimes the flooring choice will be important with the countertop choice, especially if the flooring is tile. Then it needs to work with the countertop. Wood floors tend to work with many different countertops.

Wall paint comes last, but keep your favorite wall colors in mind when picking floor tile and counters. Cool grays do not work great with warm wood tones - neither does anything for the other. A white or sage green with a gray undertone can work if you really want to go that direction. Over the long hall, warm wood tones work best if you stay with a warm look and not try to make it look like a currant gray kitchen. Also, the overuse of gray is trending out a bit, though a limited use is fine.

My kitchen is in my "my pics" idea book and I have another idea book called "wood kitchens" which has a number of mid-tone wood kitchens including some refreshed oak kitchens which might inspire as to countertop and colors. Also, a search on google images of "wood kitchens" can bring up some ideas.

I chose a more vintage / cottage style because I like it, and it works with the older cabinets:

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~110720042

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~109854029

Wood kitchen idea book:

https://www.houzz.com/ideabooks/75202366/thumbs/wood-kitchens

My sink is a Kohler Whitehaven "short apron" style apron front sink which can be installed on a standard sink base cabinet. Do be sure you like the shorter apron look before going this direction. There is also a "tall apron" style but you need a farm sink base cabinet.

One of the best things I did was add under cabinet lighting - just in my prep corner, but it brightens the kitchen and is so helpful, especially when the days are short. I started with some DIY under cabinet lighting which plugged in, and eventually an electrician wired it into a switch.

Removing a center panel and replacing with glass in doors, retrofitting a plate rail, or removing a set of cabinets and replacing with shelves are other ideas.

I have a "kitchens wood" file on Pinterest too:

https://www.pinterest.com/jeannemoy/kitchens-wood/

Excellent point, I’m already finished removing the clutter! Do you think that a mossy, darker green would work?

I would prefer not to paint the cabinets.. I feel like I have bigger problems!

I think painting the cabinets white would solve many of your issues. It would instantly make your kitchen much more current, and white cabinets would work better with the existing wall and floor colors. If painting them is an absolute no, I think there is lots of helpful advice for working with golden oak here:http://emilyaclark.com/2013/02/working-with-dark-kitchen.html (ETA correct link)

If you just want to paint walls right now then try out some colors you like buy buying sample jars of paint and try them out on foam board - place the boards around the kitchen in different lighting to help you make a decision. I would not personally go with a darker wall color because I like lighter kitchens, but everyone is different.