There are some great ideas here. My ideas:
Use a lot of baskets on top of the cabinets in the kitchen. All the same colour and size so that it looks clean and stream lined. Then pile all kinds of stuff in there that you don't use as much or that you don't have space for. Also, if everything is in a basket, it's easier to access. Instead of picking through little items, you just pull the basket down, take out what you want and put the basket back. I use baskets in cupboards that are hard to reach.
Also, I have a wardrobe that is fantastic. It holds *all* my clothes and has an extra drawer for pics and mementos. Just took a quick look. I think it's roughly 3 feet wide and 1 1/2 feet deep. There's one long drawer running across the bottom, then the rest is split in half. The right side has a long door with mirror on it that opens up and has a rod in to it hang hangers on. (With enough room for shoes to sit on bottom) Left side has 3 deep drawers where I put clothes and at the top left, a door that swings open and has 2 shelves.
I doubt there's enough room beside your door for it, but it would have been perfect.
: I got the wardrobe free from my neighbour who was tired of having it but didn't want to carry it down 3 flights of stairs to get rid of it. I think you should keep your eyes open for similar types of furniture. There's so many things you can put into it, but when it's closed up, it looks neat and tidy. Out of sight, out of mind.
Another idea is to build a separate shed to store stuff in. It can store: seasonal decorations (Christmas stuff!), clothes out of season, items that aren't used often, large toys. If you think your kids have to many toys, put some away in the shed for a month etc then rotate them. My Mom used to do that. We didn't have a lot of space growing up. It was like getting new toys all over again. (Just don't have your kids around when you pack some up).
A shed is easier and cheaper to build than an extension on the house. If can be fairly small, or a bit bigger. You could even have a work bench out there or writing desk/reading chair to get away from the kids now and then.
I remember seeing a picture of your yard. Well, the sloped wooded area behind your house. I still think a garden might be doable back there. If you can find something to use as a retaining wall and build large "steps" going down (think Aztec gardens)... I've seen it down with old railroad ties, old tires, brick/stone etc. (Just make sure that the material used doesn't have bad stuff leaching out into garden.) I can't remember if there would be enough sunlight, but you could always trim out a few trees. And while you're at it, you could make a flat patio area.
Sounds like a lot of work, but wouldn't be too bad. If you're able to do it yourself with the help of friends, and use reclaimed materials, it wouldn't cost hardly anything.