While "I says" appears often in spoken, informal speech, it is also often used as an example of extremely (excessively?) casual language -- almost a stereotype of a relaxed storytelling mode in which proper speech does not matter.
"I says" was a staple of Vaudeville comedy routines -- the fact that the speech is slightly wrong / informal helps to characterize the speaker as lower class / foolish, and make the story funnier. When you find "I says" in this kind of writing you often find it alongside a combination of informality / slang and silly grammatical mistakes, like improper verb conjugation. Popeye the Sailor also uses this kind of speech a lot, with wild grammatical errors reflecting both his lack of education and his relaxed confidence.
Here is a Vaudeville example:
I says to him, says I, “Mully, ould boy, will you have the kindness to fetch me in the mustard?” An' he was a long time bringin' it, an' I oppertuned him for kapin' me ... (Choice Dialect and Vaudeville Stage Jokes, 1902, p 109).
Currently a huge number of the recent search results hits for "I says" are all related to "so I says". These memes (including images, animations, video clips, etc.) are almost all inspired by a brief scene from The Simpsons which played on Bart using the casual, know-nothing style of storytelling that is a historical throwback to old Vaudeville: "So I says to Mabel, I says."