There is no current way to organize your items currently. Hopefully the game will implement it in a future update!! The only way I've seemed to be able to organize stuff (bugs, fish, fruit, etc..) is to use them all or sell/list them all off. Then collect them in the order you'd like them in your inventory. Also if the item you want next in your inventory isn't spawned for you, you can always buy it from a friend's Market Box.
I hope that my answer helped you out!!
There is a way to organize your items, or at least the most used items.
There are two ways you can accomplish this task. You will need a second phone (to create an alternate character) or a real physical friend to help you. Plus you will need a lot of patience, some time on your hands and attention to detail.
If you just happen to have another smart phone laying around (as I do), put it to use playing Pocket Camp. It can be any phone (Android or iPhone) that can play the game.
On second phone, download and create an alternate character. You will have to play the alternate for a while, until you're at the level where you can hold enough items and purchase enough market boxes. I would say about 18 for each (I only organized my items around the most used items. There are 18 items that the animal friends frequently request. If you don't believe me, pay attention to the game.)
After you have gotten you item level and market boxes built up, you will want to transfer items from one character to another.
Make sure you are friends with your alternate character.
You will have to clear out space in you main character's market boxes and sell everything but 1 item each in your inventory (This was the easiest way for me. You can always go back and replenish afterwards.). Also clear out all items on your alternate character. This makes transferring easier.
Before you start transferring, already have in mind how you want your items grouped.
Place 1 item each in you main character's market box. Set price to the lowest price.
On you alternate character, purchase items from main character's market boxes. You should have a clean slate to work with, you your main character.
It is worth mentioning that items appear in you your inventory as you catch or gather them. For example (Assuming your inventory is empty): you are on Breezy Hollow collecting fruit. You first pick up a peach, second you pick up a cherry and thirdly you pick up an orange. The way it's going to look in you inventory is (going from left to right):orange, cherry then peach. The next item you pick up will be placed in front of the orange (again going from left to right). Keep this in mind, while you're organizing your inventory. If you don't pay attention to this detail, your organization won't work.
Real Physical Friend:
If you have a real physical friend, that plays Pocket Camp, ask him or her to give you a hand. This is probably the easiest way because you don't have to create another character.
Sell all your inventory.
Have friend place at least one item each in his or her market boxes, at the lowest price (I hope your friend is cool and not try to make bells off you during this process, lol.)
Purchase items from your friends market boxes. Keep in mind what I stated earlier about inventory placement when items are gathered.
I know this may sound tedious and time consuming, but in the end you will have an organized inventory.
You will want to pay attention to your inventory as you are doing request and filling market boxes. Don't let any item go past one. if you do, your well organized inventory will be shot.
I hope this helps.
there is an image below how I organized my inventory. Because I couldn't share more than one pic on this post, there is a link where you can see my whole organized inventory.