That's Paper, one of Mashima-sensei characters. He's a character in Rave Master Plue's Dog Diary. In the story, he is Plue's owner.
I will tell you the characters one by one. Look at the pic.
- The white one --> Plue.
- The blue one --> Paper. He has no name, just call him Paper. He's the one appear in your question.
- The one eating banana --> Tono. He appear several times in the background of FT anime, like in Erza vs Azuma.
- The cat --> Tamiko. She's one of the cats that Gajeel found when he search for a cat. (
link) She's also appear in the anime as well.
- The granny --> Obababa-sama. In FT, Mashima-sensei made her as Lamia Scale's guild master.
- The caterpillar below Obababa-sama --> Roji. He's Tamiko's owner and Paper's rival. He's kinda like the antagonist of the series but he's really funny as hell.
The rest are minor characters.
Well, that's it. They appear often in Fairy Tail. Example, in the episode Lucy vs Bickslow. After Sagittarius destroy Bickslow's dolls, he immediately get new dolls, which is the dolls of Roji, Paper, Tamiko, Obababa-sama, and the bear (Kuma). And like I said before, some of them also appear often in FT's anime background (Paper and Tono).
So, stop calling them 'weird creatures' (well, all of them are weird, that's true). But still, they're Mashima-sensei characters :)