Burletero is a colloquial term, especially used in the Canary Islands (where Cruz Cafuné is from), meaning someone who is a joker, a mocker, or someone who makes fun of others.
In the song, the line "El niño de la isla se pasa de burletero" translates to "The island boy is too much of a joker/mocker." It captures a playful yet slightly critical observation of someone's personality, making it an interesting and regionally specific word.
Mi Casa is a party story told by someone having far too much fun at a house that is not his. Cruz Cafuné turns up late and already high ("Hoy empecé a fumar antes de tú estar despierta" [Today I started smoking before you were even awake]), carrying only a bottle of wine and some papas (Canarian for potatoes or chips). The chorus is pure relief: "Menos mal que no es mi casa" [Thank goodness it's not my house], repeated until you can picture the mess.
The song is packed with Canary Islands slang. Chacho is the islands' all-purpose "man!" and fiolos are mates. "Clipper de fresa" [strawberry Clipper] is a soda from the Canaries, so people see his red cup and assume it is innocent. One guest introduces herself as "Candela" with the surname "Fogalera" (a bonfire), a joke about being on fire, and he keeps teasing a girl: "¿Pero tú no eras lesbiana?" [But weren't you a lesbian?]. It is loud, cheeky and a bit much, which is exactly the point.