You should:

1) Post a to-scale floor plan. I know it's a lot of work to make one, but the quality and applicability of the help you'll get as a result is a LOT higher. Print an image of graph paper from the internet and draw it by hand or copy an image of graph paper into MS Paint and draw the floor plan there.

2) Define your budget. Are we talking $500 or $10,000?

you could slide in cabinetry and counter between washer/dryer and water heater.... as well, you have space near fridge..move the fridge away from door and cabinet/counter to left of fridge as landing spot. With a drop leaf table you could install cabinets under window to right of door [in dining zone] to store china and dishes all sorts if you want. Look for the right kind of table so you can use that wall in dining zone..... that would be my first activity as you get to find something vintage and different, not too expensive.

I would swap the fridge and stove. It would be helpful to know how much work you want to do - are you replacing cabs/countertops and re-arranging things or just trying to add to what you have to make it more functional?

I was thinking the same thing about the fridge/stove.

I'd have probably a 2-3K to spend, and we would be doing most of the work ourselves. I have no problem scouring Craigslist for counter remnants, used cabinets, etc. Thanks!

I agree with the posters who suggested switching the fridge and stove. I would also consider an undercounter/inline water heater, and get rid of the hulk in the corner. Then you could have a corner susan for pots and pans.

Have you thought about adding a short wall to form a hallway to separate the bathroom and one of the bedroom doors from the kitchen? You could make the framing deep enough to incorporate storage between the studs for canned goods and boxes. I have a between-the-studs pantry in my older home, and it holds a lot of canned goods and jars. Actually, I have a hallway the same size, too, with doors to a walk-through pantry, bathroom, and master bedroom, but it's off the dining room.

Can the water heater be moved outside?

I think the question is too broad. What needs fixing? Do you want to re-arrange? Change the "feel" through decor/paint? Find more storage? Hide something? etc.

If you are not moving anything, I'd add hooks to the wall beside the stove for potholders/spatula/etc. A cabinet or shelf of some sort might be nice to the left of the stove as well. I would put those little shelves on each side of the cabinets on either side of the window for storage, or a hanging basket (if you use those). For more $$, possibly switch out to track lighting so there is more light over your stove area, or see if a fixture can be added within your budget.

I imagine moving the WD further into the house and away from the plumbing will get expensive. I would suppose that it uses the plumbing in that wall. Does the bathroom plumbing wall back up to the water heater? (How nice, not water instantly in the shower!). If the sink and toilet are on the outside wall, though, could you steal space from the bedroom and extend the bathroom into there, and install the W/D there?

That way you can have the fridge next to the water heater, the range where the fridge used to be, and storage/coffeemaker/electric kettle/etc where the stove is now.

or, range where the w/d were, fridge where the stove was, and more counterspace where the fridge was.

I'd explore getting the washer and dryer and water heater out of the kitchen.

If you live in a mild climate, you might look into a tankless hot water heater installed outside. We did that and it's been awesome, both in terms of reclaimed space and never running out of hot water. It's not cheap, but I think it would make a big difference.

There are some washer and dryer all in one machines. I don't know much about them, but I have the impression they aren't optimal. But with a smaller place, I'm guessing this isn't for a big family so maybe those trade offs would be worthwhile?

We had a very small kitchen in our first house. We remodeled but kept and painted the cabinets. Everything else was new, including all new appliances (the old ones were not working well anymore and were brown, black and white). We installed glue less click cork flooring, granite tile counter tops, and new lighting. We also took down two useless upper cabinets and replaced them with open shelves and a pot rack. That was about 16 years ago. We spent somewhere around 5k and did all the work ourselves except we paid a plumber to install our dishwasher and new faucet.

General space saving/storage maximizing ideas (some may be too expensive or not work in your space): pot racks, cabinets to the ceiling, as many drawers as possible for lower cabinets, smaller appliances (18 inch dishwashers and small refrigerators--LG makes a 24 X 24 model--in particular), toe kick drawers, storage space built in between studs.

if you provide a drawing to scale on graph paper, the kind people here will give you all sorts of free suggestions I am constantly amazed at how generous posters here are with their time and ideas

Is this your own home or a rental? If it's your home, are you planning to stay long?

I would look into the cost of switching to a tankless water heater, that saves a lot of space and would give you a lot more counter space and storage.

If the washer/dryer and water heater can be made to miraculously disappear (or be moved to the bathroom/wh outside), I'd put the stove on the short wall, fridge on the exterior wall, and put a pantry beside the furnace closet:

Can the door near the dining table be moved to the right giving you more usable wall space in the kitchen?