Making the rest of your characters gives you more inventories. I am a notorious hoarder and I usually sell everything that is reorderable because I know that bells are easy to make, and if I know I am actually going to use the items I'll keep THOSE in my inventory, such as tree and bush starts, and all of my tools, and the furniture I know I am actually going to put out when I get my house done.
Saved mail. Group up your stuff. Make a list on paper saying ex: A-1: street pass balloons A-2: Gracie hats etc... You can store 180 more items in saved mail.
I use the museum rooms for things like bush starts, tree starts and flower bags because you can walk over them so you don't have to move stuff around to get to a specific thing. Sell everything that's orderable and use a second character to hold on to unorderable items that I want to keep. It's still not a lot of room but it works.
I would say sell (giveaway) Gracie furniture sets unless you use them because you know you can always reorder them when the season comes around.
It's not like they're only available for 1 day or 1 event, plus it helps save a lot of room. 13 pieces x 4 or 5 sets (if you count card set) and you don't have to worry about 52 to 65 pieces taking up space.
You could also do that with the Gracie clothes she sells but that's up to you.
I'm quite the opposite when it comes to storage. I regularly clean out and sort my storage so it isn't cluttered. I sell or get rid of anything I don't plan on using in the immediate future, save for those few exceptions like tools and such.
You could try my mom's method of storage: letters. She puts items in empty letters and then saves them at the post office. It can be an effective way to store items, if you're willing to take the time to sort them for easy reference later.
You could also use Re-Tail. It won't hold lots of items like letters can, but it's an easy way to open up 8 spaces (9 spaces if you count Cyrus) in your storage.
Another method, which has been mentioned already, is keeping stuff in the Museum. I personally prefer keeping sets in the rooms, but you can put anything in the rooms. My mom used to keep gyroids in hers.
I just sell everything that's reorderable and only keep the unorderables I want/really need. Also make full use of your museum rooms.
I have everything I need in my closet space, and I only have one character. There's some stuff along my beach, but that's everything I'm selling to others.
At the end of the day, once your house is exactly the way you want, do you really need unorderables except to catalog?
I keep most of my bush starts/furniture sets in the museum displays lol
I'm thinking of making another character soon so I can have more storage as well.