I fished in each of the game's 5 portals 50 times. Some items are common to all portals while others are exclusive to one. This is empirical data so I'm sure I've missed items. In fact, I have 7 spots still empty in the museum, so I *know* I've missed some.

All fishing was done during a Waning Moon, though I don't think the moon phase affects this.

Items in bold are used in a quest; items in italics are used as a gift.

• Air Freshener - Witch's House
  
• Banana Peel - Town, Crystal, Swamp, Cloud
  
• Bell - Witch's House
  
• Block of Tofu - Swamp
  
• Blue Ribbon - Swamp2
  
• Bottle Cap - Witch's House, Town, Swamp, Cloud
  
• Broccoli - Witch's House, Town, Crystal, Swamp
  
• Carved Pumpkin - Swamp
  
• Cassette Player - Swamp2
  
• Claw Clip - Crystal
  
• Computer Chip - Crystal
  
• Credit Card - Cloud
  
• Cryptid Figurine - Swamp, Cloud
  
• Dagger - Swamp
  
• Deodorant - Cloud
  
• Dragon Scale - Crystal
  
• Electrical Component - Swamp
  
• Essential Oil Burner - Crystal
  
• Feather - Witch's House, Town, Crystal, Swamp, Cloud
  
• Hand Mirror - Swamp2
  
• Headset - Cloud
  
• Incense Stick - Swamp2
  
• Lemon - Swamp
  
• Lightbulb - Crystal
  
• Lip Gloss - Cloud
  
• Moss Ball - Witch's House, Town
  
• Paper - Witch's House, Town, Crystal, Swamp, Cloud
  
• Phone - Witch's House, Town
  
• Plushie - Cloud
  
• Propeller - Swamp2
  
• Purple Candle - Crystal
  
• Red Candle - Cloud
  
• Remote - Cloud
  
• Rocket Engine Nozzle - Swamp2
  
• Rocket Nose - Swamp2
  
• Rose Petals - Witch's House, Town
  
• Seat Belt - Crystal, Swamp
  
• Skull - Town, Swamp
  
• Solar Panel - Cloud
  
• Tea Set - Witch's House, Town
  
• Tin Can - Swamp
  
• Toilet Seat - Town
  
• Totem - Crystal
  
• Unicorn Hair - Crystal, Cloud
  
• Unicorn Horn - Crystal
  
• USB Stick - Swamp
  
• Weird Bone - Cloud
  
• Wood - Witch's House, Town, Crystal, Swamp, Cloud
  
• Yellow Candle - Town

Obviously the most common items are those that are found in multiple locations: Paper, Wood, and Feather. The only other item that appeared more than 15 times out of my 250 casts was Rose Petals, since 11 of the 50 Town catches were Rose Petals.

The items with 2 or fewer catches are: Computer Chip, Dagger, Deodorant, Dragon Scale, Essential Oil Burner, Headset, Purple Candle, Red Candle, Yellow Candle, Seat Belt, Solar Panel, Tin Can, and Unicorn Horn.

I got Message in a Bottle and Newspaper from the Cloud portal, but that is likely due to where I fished after progressing a quest. Likewise, I got To the Mages of Corbin from the Crystal portal.

An unknown computer-looking/rocket ship part came from a non-Cloud portal.

I didn't fish it up in my trials, but I had donated it prior to unlocking the Cloud portal.

The Swamp2 portal is only accessible after the credits. Other items may be available from there, but the unique ones are listed above. Thanks to @Voron for the details.