From the Super Mario Wiki
As the name suggests, Tweeters are possibly some type of bird-like being. Though its mask seems to have a beak, it could also be intended to look like a long nose, suggesting it could have been based off of a Japanese mythical creature known as the Tengu. This possibility is far more present in the earlier designs of Tweeters, having distinguishably red masks, similar to a Tengu's common depiction of a red face. Since they are recolored pink in Super Mario All-Stars design, however, their resemblance to a Tengu is significantly smaller.
Super Mario Bros. 2
Tweeters made their first appearance in Super Mario Bros. 2 as common enemies throughout the game. Although they have wings, Tweeters cannot fly; however they are very good at hopping across the ground (acting very much like Paratroopas). Tweeters (like Shy Guys and Ninjis) are easy to pick up and throw at other enemies.
The Super Mario Bros. Super Show!
Tweeters made several appearances in The Super Mario Bros. Super Show!, were they were usually portrayed as minions of King Koopa. The first appearance of a Tweeter was in the episode "Butch Mario & the Luigi Kid." In this episode, a Tweeter bounty hunter, dressed as a cowboy, acted as an informant of Sheriff Mouser, telling him and his minions the location of Mario, Luigi and Toad, in exchange for Gold Coins. A sub-species of Tweeter called the Tweeter Bat appears in the episode "Count Koopula". In the show, the Tweeter's color scheme is inverted. In The Unzappables, a tweeter can be seen when Mario is looking for a stool pigeon, to give away Koopone's plans.
A Tweeter appears in volume 8 of Super Mario-Kun. Here, it attempts to puncture Mario's hat, only to have Mario transform into Dr. Mario.
Nintendo Adventure Books
When Mario first arrives in the Mushroom Kingdom in Double Trouble, he spots some orange Tweeters (most of them presumably sand clones created by the GLOM) fighting for room on a brick ledge; later, Mario mentions that he hates it when Tweeters try to land on his hat.
If Mario and Luigi follow Princess Toadstool to the Koopahari Desert in Pipe Down!, they will be attacked by a flock of Tweeters, which will also appear to attack the Mario Bros. if they pull the mushroom lever in an elevator in the Mushroom Palace, if they try to directly attack Ludwig von Koopa during one portion of the book, and if Mario pulls the wrong nob on the Koopaling's giant pipe organ.
Super Mario Bros. film
In the Super Mario Bros. film, a street vendor can be seen selling and advertising Fried Tweeter, apparently cooked Tweeters; instead of birds, the film portrays them as lizards. They are eaten on hotdog buns.
Mario Kart Super Circuit
Tweeters made a small cameo in Mario Kart Super Circuit, they were found on the totem poles on the track of Sunset Wilds. The Tweeters on said totem poles look very similar to the new versions of Shy Guy and Snifit; as it looks like a Shy Guy with a Tweeter mask. 
Super Mario World 2: Yoshi's Island
Names in other languages